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 Topic: linear
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A rectangular garde 2020-04-10
From Denise:
In a rectangular garden a person says "if I made that bed 2 feet wider and 3 feet longer it Would have been 64 sq,ft bigger. But if it had been 3 feet wider and two feet longer It would have been 68 sq.ft bigger.
What is the length and width of the garden bed?

Setting up a linear equation 2020-04-10
From Jessie:
Michaela and Aleah play on the same basketball team. In one game, Michaela scored one fifth of the teams points and Aleah scored one tenth of the teams points. Together, they scored a total of 42 points. How many points did the team score?

I can't figure out how to put together the equation with the given variables. I have to show the work and I also need to know how to make that kind of equation. Thanks!

A linear system 2020-04-02
x+s=8→1
y+x=13→2
y-p=6→3
s+p=8→4

The equation of a line 2020-01-05
From coco:
Good afternoon If relationship between total cost and the number of units made it linear ,and if costs increases by 7\$ for each additional unit made ,and if the total cost of 10 units is 180\$ .
Find the equation of the relationship b/n total cost (Y) & number of unit made (x).

Simultaneous equations 2019-10-16
From deepak:
8/x - 10/y = 1 and x+y=9

Two power generators 2019-06-07
From A student:
At 100% efficiency two generators would produce 750 MW of power. At efficiencies of 65% and 75%, they produce 530 MW. At 100% efficiency, what power would each produce?
Two linear equations with a fraction 2019-04-26
From Asha:
2x=-3y …1
x-2+-4/3(y+1) ...2

note: … is equation

A linear equation 2019-02-11
From Nick:
What's a linear equation?
Simultaneous equations with fractions 2018-12-14
From zaheer:
solve simultaneous equations and give answer in fractional form
3x - 2 = 4y +5/3
y + 7 = 2x + 4
would really appreciate some help on this please

Linear feet and cubic feet 2018-07-16
From Dave:
How do I convert: 1 foot wide x 15 inches high x 19 inches deep

We are trying to figure out how to convert the linear footage into cubic footage the above are the figures represent just 1 linear feet of several thousand

Any thing helps,

Dave

Simultaneous equations with fractions 2017-09-09
From Farah:
Hi, my name is Farah. I hope you can help me with this question . X/2 + g/5= 3 and 2g - f = 10
A pair of linear inequalities 2017-08-08
From Hempstone:
Solve the inequalities 3x-5<2x+5>4x+9
Catherine, Molly and Tom 2017-07-19
From liezel:
what is the answer of this problem, If Catherine and molly has 320pesos altogether, Molly and tom have 360 in all. Tom and Catherine have 240pesos altogether.How much does each of them have?
Simultaneous equations with fractions 2017-06-02
From Jamal:
1/x + 1/y =5 and 1/y - 1/x =-1
Five equations 2017-01-16
From Muhammed:
A x 4 = E
B ÷ 4 = E
C + 4 = E
D - 4 = E
___________
& A + B + C + D = 100
what is the value of E

Simultaneous equations with fractions 2016-12-21
From Kimi:

1/2x+1/3y=11
8x+2/5y=102
Can someone please explain how to solve questions like these?? Or else I will never learn...
Thank you

Simultaneous equations 2016-11-25
From Rohan:
x-2/3 + y - 1/4 = 13/12
2-x/2 + 3 + y/3 = 11/6

A linear relationship 2016-10-16
From Bianca:
x represents the number of hours since 8am. y represents the number of children the school nurse has seen during the school day. The nurse has seen 3 children by 8am and 27 children by noon.
How many children has the nurse seen at 2pm?
If the nurse has seen 18 children, what time is it?

The length of stock on a roll 2016-09-23
From Ken:
I have a roll that is 13.5 inches wide ( OD) , and is wound on a 3 inch core. the thickness of the material is 3.5 thick.
Do you know of a formula that can calculate the linear feet on that roll??

The dimensions of a rectangle 2016-07-25
From Krunox:
A rectangle is twice as long as it is wide. Its perimeter (the sum of the lengths of its sides) is 60 cm. Find its length and width.
The temperature inside and outside a greenhouse 2016-07-22
Every day, the temperature in a greenhouse is at its low temperature, 70 degrees Fahrenheit, at 2 a.m. and at its high temperature, 84 degrees Fahrenheit, at 2pm. Its temperature increases linearly between 2 am and 2pm , and decreases linearly from 2 pm and to 2am. The outside temperature follows the same linear patterns, but has a low temperature of 60 degrees Fahrenheit at 2 am and a high temperature of 78 degrees Fahrenheit at 2 pm. At which of the following times will the temperature inside and outside the greenhouse be the same?

a) 8:00 am
b) 12:00 noon
c) 4:00 pm
d) The two temperatures will never be the same

Two equations with fractions 2016-07-22
From kanesh:
p/2+q/3=3

p/4+2q/3=3

Simultaneous equations 2016-06-25
From sena:
2x/3+3y/2=-1
4x-5y=22

simultaneous equation

A pair of equations with fractions 2016-05-11
From tiya:
hello, i want to know how to solve this question.

m/6+2n/3=6
-m/10=2n/5=2

Solve for x and y 2016-02-27
From ntshidi:
Y=1/2x+4and1/4x-6
Two equations in two unknowns 2016-02-13
From Anumba:
4x + 2y = 4
7x - y = -11

A system of linear equations 2016-01-24
From kareem:
my name is kareem
and i am a student i have a math puzzle and i tried to solved it but it always have same mistake
x-y=9
x+z=12
z-n=14
y+n=2

Two transport companies 2016-01-06
From Brynleigh:
The Sugar Sweet Company will choose from two companies to transport its sugar to market. The first company charges \$5096 to rent trucks plus an additional fee of \$200.75 for each ton of sugar. The second company charges \$5500 to rent trucks plus an additional fee of \$175.50 for each ton of sugar. For what amount of sugar do the two companies charge the same? What is the cost when the two companies charge the same?
A graph of the water level of a river 2016-01-05
From emoni:
Suppose that the water level of a river is 34 feet and that it is receding at a rate of 0.5 foot per day.
Constructing simultaneous linear equations 2015-12-28
From Deborah:
Linda thinks of a two-digit number. The sum of the digits is 8. If she reverses the digits, the new number is 36 greater than her original number. What was Linda's original number?

Thank you!

Linear equations in two variables 2015-12-13
From priya:
I)2x+y=y
II)pie*x+y=9

The method of elimination 2015-05-01
From oreanna:

Question from oreanna, a student:

How do u solve 2x+9y=3

7x-4y=-25 in elimination

Two equations with fractions 2015-02-26
From Pulane:
(9/x)+1=(-2/y)

Thank you

Two equations 2015-02-16
From nigel:
2x+1/2y=1
6x-3/2y=21

1999 equations in 1999 unknowns 2014-11-28
From Subrahmanya:
Solve the following system of 1999 equations in 1999 unknowns :

x1+x2+x3=0, x2+x3+x4=0……., x1997+x1998+x1999=0,

x1998+x1999+x1=0, x1999+x1+x2=0.

(in x1,x2,...................,x1999 the numbers 1,2,.............,1999 are subscripts)

From rajesh:
Sir,
I would like to discuss on question-
-Find the value of variable X and Y, equations are
X2+Y2+2XY=25
X2+Y2-2XY=1

Sir, my point is equation looks not so easy.My opinion is there many (more than 4)value possible for both X and Y.
Kindly help me.
regards,
rajesh

A linear system 2014-10-14
From pheter:
4/x - 1/y = 3 .... equation (1)
6/x - 2/y = 5 .... equation (2)

Two equations in x and y 2014-09-25
From seyilogo:
solve y=2x - 3 and (4x - 2y) / x + y = 1 simultaneously
Two equations in two variables 2014-09-18
From Susan:
(28x + 36y) - [20000 - .75(28x + 36y) + 60000] = 5000
x + y = 10000
solving two equations involving variables

Three collinear points 2014-08-28
From jhanavi:
p,q,r are three collinear points.p and q are(3,4) and (7,7) respectively and PR is equal to 10 units.find coordinates of R
The method of elimination 2014-07-05
From leo:
please explain how can i solve this problem

3x-6y=-38
6x-9y=44

using elimination and simultaneous method thank you :)

Simultaneous equations 2014-06-20
From rana:
solve the simultaneous equations
a)3x=7y
12y=5x-1

Two regression lines 2014-06-14
From catherine:
Given a set of data values ,we can get two regression lines .Explain.
Answered by Robert Dawson and Penny Nom.
A trig problem 2014-04-25
From srishti:
Consider the points P= (-sin(a-b),-cosa), Q=(cos(a-b),sina), R=(cos(a-b+c),sin(a-c), where 0
Simultaneous equations with fractions 2014-04-19
From Maryam:
I looked at your example of simultaneous equations with fractions and applied it to my question from an educate exam papers but I couldn't get it to work. The question is:

x/8 - y = -5/2
3x + y/3 = 13

Two nonlinear equations 2014-01-26
From Naryn:
(1÷x) + (1÷y) = (7÷12)
xy = 12

A linear equation 2013-12-26
From khushboo:
A farmer sowed wheat and paddy in two fields of total area 5000 sq.m. Write a linear equation and draw a graph to represent the same?
How do I graph y=-2x-1? 2013-12-07
From cindy:
How do I graph y=-2x-1?
A line through (5, 1) 2013-10-08
From allison:
find an equation in standard form for line passing through point (5,1) and perpendicular to line x=4
A system of equations 2013-08-13
From Nina:
3x-2y=8
-x+3y=5
What is the solution of the system of equations

4 linear equations with 3 unknowns 2013-04-12
From Marian:
how to solve for 3 unknowns in 4 simultaneous equations
A linear programming problem 2013-02-27
From Kelley:
A manufacturer of skis produces two types: downhill and cross-country. Use the following table to determine how many of each kind of ski should be produced to achieve a maximum profit. What is the maximum profit? What would the maximum profit be if the time available for manufacturing is increased to 48 hours.
Downhill Cross-country time available
manufacturing time per ski 2 hrs 1 hr 40 hr
finishing time per ski 1 hr 1 hr 32 hr
profit per ski \$70 \$50

A geometry word problem 2013-01-24
From Matthew:
"G", "A" and "B" are collinear. "A" is between "G" and "B". "GA" Is 14 less than 3 times "AB". "GB"=46 Find "GA"

How would you solve this?

A word problem involving a fraction 2012-10-12
From Derrick:
If the numerator and denominator of a fraction are both decreased by 1 the fraction becomes 2/3. If the numerator and denominator are both increased by 1 the fraction will be 3/4. Find the original fraction. How to do?
A problem that yields a linear equation 2012-10-07
From Eshraj:
one fourth of a whole number is three more than one fifth of the next whole number.find the whole number
Row echelon form 2012-09-05
From Jennifer:
Hello, my name is Jennifer. I am a 12th grader in Pre-Calculus and I was wondering if you may help me with Row Echelon Form.

x + 2y - 3z = -5
-2x - 4y - 6z = 10
3x + 7y - 2z = -13

Problem solving 2012-08-15
From Sugavanas:
If length of a rectangle exceeds its width by 5 m. if the width is increased by 1m and the length is decreased by 2 m, the area of the new rectangle is4 sq m less than the area of the original rectangle. Find the dimensions of the original rectangle.
John's electronic store 2012-07-25
From Jora:
Electronic Store John opened an electronic store in December. During his first month, He sold 10 LCD TVs and 20 Plasma TVs. His income during that month was \$12800. In January, he sold 25 LCD TVs and 40 Plasma TVs for an income of \$27600. In February he projects to sell 30 LCD TVs and 50 Plasma TVs. If John expenses are \$28900 in February, how much money will he have after paying the expenses?
2x+underroot2=3x-4-3underroot2 2012-07-09
From Eshraj:
2x+underroot2=3x-4-3underroot2
The equation of a line 2012-03-26
From Danielle:
Hello, could you help me figure out what the equation of the line is in the form of Ax+By=C with the points (-2,0) and (0,3)? Thank You!
Four apples and two oranges cost Rs. 30... 2012-01-13
From nasr:
Four apples and two oranges cost Rs. 30, and one apple and 3 oranges costs Rs.15.How much does each apple and each oranges cost?
Augmented matrix 2011-12-14
From Britney:
Write Augmented matrix and use row reduction to solve.
I need major help with this problem! Tomorrow is my semester test and I have no idea how to do this.
2x+5y=8
y-x=10

Linear equations 2011-10-06
From Hannah:
I am confused about a question on my homework, here is an example on what I need to do:

You own a sightseeing boat tour. Kids' admission costs \$5, adults' admission costs \$8. During that day you get (made-up number) \$521 with 71 admissions. How many of each passenger boarded?

I tried something like
5x + 8y = 521
x + y = 71

But, I still don't understand how to solve it! Help?

An equation in the form Ax+By=C 2011-07-28
From Mike:
I need to write an equation in the form Ax+By=C The points I was given are (5,0) and (-3,5)

I know how to find the slope I got -5/8 and wrote it out as y=(-5/8)x+b however I'm not quite sure where to go from here.
Any help would be greatly appreciated.

A linear equation with fractions 2011-07-13
From Simon:
I would like to ask if you would be able to explain : linear equation: 2 1/2 (X-1) - x+3 /3 = 4 , the first step shows multiplying by 2 then multiplying by 3. etc. What I don't understand is where the 2 in multiplying by 2 comes from? ( the three is pretty obvious being x+3 /3 (to get rid of the divided by) ) .

Linear inequalities 2011-03-25
From Alice:
OK. I'm in algebra 1 and the linear inequality is
y<2x-1
y>2
I don't completely know how to graph y>2 and I'm getting really frustrated
Thank You!

What is the speed of each car? 2010-11-04
From Jennifer:
two cars are 420 miles apart and traveling towards each other along the same road. They meet in 3.5 hours. One car is traveling 15mph slower than the other. What is the speed of each car? This must be solved using a system of equation, I have no idea?
An exponential equation 2010-10-19
From Sandi:

Question from sandi, a student:

I have several questions similar to this one and was wondering if you could walk me through this one. I'm totally lost on how to do it.
Paramecia reproduce by splitting in two. In a laboratory flask, a colony of paramecia had an initial population of 500. Each day, the population of the paramecia was counted. The results are as listed.
Time (in days)------Population
0-----------------------500
1-----------------------600
2-----------------------720
3-----------------------864
4----------------------1037
5---------------------1244
6---------------------1493
7----------------------1792
8---------------------2150
1.)Using graphing calculator make a scatter plot of the data in table.
I think I did this part right I set my window at Xmin=0 Xmax=10 Xscl=1 Ymin=0 Ymax=2500 Yscl=100 Xres=1
2.) Determine an exponential equation to represent the population as a function of time without using a graphing calculator.I have no clue how to do this.
3.)Suppose the flask and food supply is large enough to support the trend of the population growth. Estimate the population of the colony when the time is 10 days.

A linear system 2010-10-15
From Sandy:
HARD!! algebra (Linear Systems) question? An Airplane cruises at 120km/h in still air. One day, when the wind was blowing steady from the west, the airplane travelled west (flying into the wind) and landed at its desination after 1.5h. The airplane's return trip (flying with the wind) was only 1.0 h long. On both legs, the airplane travelled at its cruising speed. (meausred with respect to the air surrounding the airplane).

Part A
Write a System of equations that would allow you to determine the speed of the wind blowing that day and the distance travelled each way

Part B
When solving the system of equations graphically, what equations would you enter into the equation editior (to make graphs on your calculator)

Part C
Indicate what the X and the Y represent

A strip of land 2010-09-15
From Walter:
How many linear feet of strip of land 15 feet wide does it take to make 1 acre?
A linear relationship 2010-06-22
From Laura:
The monthly cost of driving a car depends on the number of miles driven. Lynn found that in May it cost her \$300 to drive 480 miles and in June it cost her \$460 to drive 800 miles.

Question: Express the monthly cost C as a function of the distance driven d, assuming that a linear relationship gives a suitable model.

4 > -3m-7 >= 2 2010-06-05
From pamela:
The question is
4>-3m-7>=2

x/a +y /b =a+b : x/a^2+ y/b^2 =2 2010-05-30
From smithu:
x/a +y /b =a+b : x/a2+ y/b2 =2 solve by using elimination method , cross multiplication, substitution method
Graphing a linear inequality 2010-05-26
From Valeie:
When graphing a linear inequality, how do you know if the inequality represents the area above the line.
A system of equations 2010-03-30
From samantha:
the equations of two lines are 6x-y=4 and y=4x +2.what is the value of x in the solution for this system of equations?
The sides of a 30-60-90 triangle 2010-03-29
From maris:
Find the sides of a 30-60-90 triangle whose perimeter is 6. The solution must use systems of equations using 3 variables.
From rachelle:
under certain condition, it is found that the cost of operating an automobile as a function of speed is approximated by a quadratic equation. use the data shown below to find the function. then use the function to determine the cost of operating the automobile at 60mph.
speed
(in miles per hour)
operating cost
per mile(in cents)
10 22
20 20
50 20

The line joining (3,4) and (-5,-6) 2010-03-06
From Patric:
Find the condition that the point (x,y) may lie on the line joining the points (3,4) and (-5,-6)
A linear relationship 2010-02-24
From Mel:
This table shows the linear relationship between an aeroplane's height (above sea level) and the outside air temperature.
 h (cm) 120 340 480 600 1040 T (degrees C) 14.28 12.96 12.12 11.4 8.76
Find the gradient and vertical intercept of the function. Write the formula for T.

Substitution method 2010-02-17
From Melodie:
7x - 4y = -10
4y= x-2

Substitution 2010-02-14
From Izayah:
what is 3 ways to find the meeting point of y=2x+4 and 3x+y=7 by making 2 table and using a graph
Linear growth 2010-01-27
From S.:
I. Linear Growth:
Suppose that the town has a fixed increase in population growth number of population increase each year.

Choose the amount of population growth each year = 200 (Hint: Choose a whole number for your growth rate, rather than a percent.)

a) Fill in the following chart:

Year (t) Population (P)
t = 0
(2010) 1000

t = 1
(2011) 1000+200=1200

t = 2
(2012) 1000+400=1400

t = 3
(2013) 1000+600=1600

b) Find a linear equation in the form P = mt + b (y = mx + b), which gives the population, P, t years from 2010.

.
.
.

A linear equation with the variable on both sides 2010-01-16
From dog:
4x-9=7x+12
A linear equation with fractions 2009-12-31
From Michelle:
How would I solve: (-2)(-1/2x + 5) = (-2)(8)?
Linear programming using the Simplex Method 2009-12-28
From William:
A gold processor has two sources of gold ore, source A and source B. In order to keep his plant running, at least three tons of ore must be processed each day. Ore from source A costs \$20 per ton to process, and ore from source B costs \$10 per ton to process. Costs must be kept to less than \$80 per day. Moreover, Federal Regulations require that the amount of ore from source B cannot exceed twice the amount of ore from source A. If ore from source A yields 2 oz. of gold per ton, and ore from source B yields 3 oz. of gold per ton, how many tons of ore from both sources must be processed each day to maximize the amount of gold extracted subject to the above constraints? I need a linear programming solution or algorithm of the simplex method solution. Not a graphical solution. Thanks.
Two non zero vectors 2009-10-27
From Nazrul:
Given that a and b are two non zero vectors and ma+nb=0 where m and n are two scalars. How can I prove that m=n=0.
A word problem 2009-10-24
From Ryan:
Two times one number plus 7 times another number is equal to 17. the first number plus the second number is equal to 25. What are the two numbers? Please Help!
A linear system 2009-10-20
From marissa:
Solve this linear system
2x-y=5
3x+y=-9

\$6.25 in nickels quaters and dimes 2009-10-10
From miriam:
a piggy bank contains \$ 6.25 in nickles quaters and dimes. there are 65 coins all together and there are four times as many nickles as quaters find the number of coins of each kind
Two rectangles 2009-10-08
From Lillian:
A rectangle is 5cm longer than twice its width. The width of another rectangle is 3cm less than the width of the first rectangle and its length is 6cm more than 3 times its width. If the perimeters are equal, find the dimensions of both rectangles
Elimination method 2009-10-08
From Kenty:
How do I solve this problem using the elimination method?
3x-7y=0
6x+4y=0
I am not sure how so if someone can show me a similar problem (instead of solving this one for me) that would be fantastic.

The method of substitution 2009-09-17
From laura:
ok! i really need help with this question plz help!!

x= - 4y +5
x+2y = 7

10x-8 /3 =6x+24 /5 2009-09-16
From Heidi:
10x-8 /3 =6x+24 /5.....I know the answer is 7/2 but how do I get there?
Simultaneous equations 2009-08-28
From onias:
solve 3/a - 2/b = 1/2 , 5/a + 3/b = 29/12
y=2x+1 and y=2x-1 2009-08-28
From MARICELA:
Need help of how to work this problems

y=2x+1 and y=2x-1

First of all what is the difference?

Second I think is easy just to work with the X y with the line in the middle

but how do you get the numbers for each side.

Linear equations 2009-08-23
From shwetha:
The length of a rectangle is greater than the breadth by 18 cm. If both length and breadth are increased by 6 cm then area increases by 168 cm square. Find the length and breadth of the rectangle.
Graph 2x-3y+15=0 2009-08-20
From Diem:
Graph 2x-3y+15=0
Two equations in two unknowns 2009-07-30
From Alicia:
I need help with the following equation please show me the steps to complete so that I will know how to do this my self.
2x-y=2 5x+y=5 Thanks for the help

Finding the Line Joining Perpendicular Feet 2009-07-16
From mukulu:
Please help I've been tryng to search in your data but i failed to get the solution Find the equation of a straight line joining the feet of the perpendiculars drawn from the point A(1,1) to the line 3x-3y-4= 0 and 3x+y-6=0.
Two equations 2009-05-31
From tony:
y = 1.2x - 32.7,

y = -0.7x + 46.15

can you please solve this for me? i am not able to figure it out... thank you tony

(x + 1) / 3 + (x + 2) / 7 = 2 2009-05-22
From MzDonna:
Question from MzDonna, a parent:

We can't seem to get an answer for this problem:
X + 1      X + 2
_____ + _____   = 2

3              7

___
21

Two equations 2009-05-18
From Bob:
solve the system:

x/2 - 2y= -8
3x + 2/3y= -10

Finding an Array to an Integer Linear Programming Problem 2009-05-12
From Debbie:
how to make an array for 3 box of juice for 25 students and 2 teacher. 1 pack of juices hols 3boxes the answer is 9 packages but how do you make array for this
Solve -1<5-2x<10 for x 2009-05-12
From Helen:
solve the following inequality for x
-1<5-2x<10 Te less then sign by the one, should be less then or equal to.

Answered by Stephen La Rocque and Penny Nom.
Stairway construction 2009-05-02
From Olivia:
Hi, I'm Olivia and I'm in 8th grade studying algebra 1. I'm having some trouble with my math project. It has to do with rules of stairway construction. It says that there are two generally accepted rules to building stairs. Rule 1: x+y=43 and x+y=46 (cm) Rule 2: 2y+x=61 and 2y+x=64 (y is the riser and x is the tread length) I cant figure out how to graph them...it says they're supposed to intersect to make a square which is like the safety zone for building stairs (the stairs' rise and tread lengths are plotted as points) any points outside of that square are considered unsafe. Did i explain it ok? Thanks for your help. --olivia
An infinite number of solutions 2009-03-24
From Sean:
this is a linear equations problem;

first:
3535.5 + Fbd (.866) + Fbc (.5) - Fab (.5) = 0
and
-3535.5 - Fab (.866) - Fbc (.5) - Fbd (.5) = 0

A dead fly is stuck to a belt that passes over two pulleys 2009-03-21
From Jules:
A dead fly is stuck to a belt that passes over two pulleys 6 inches and 8 inches in radius. Assuming no slippage,how fast is the fly moving when the large pulley (8 inches) makes 21 revolutions per second ? How many revolutions per second does the small pulley make ? How long will it take the dead fly to travel 1 mile ?
A linear system 2009-03-13
From Rasanga:
Use the row echelon form of the augmented matrix to solve the following linear system.
X1+2X2+X4=6
X3+6X4=7
X5=1

Find an expression for the nth term 2009-02-20
From Dawn:
Find an expression for the nth term:

x= 1 2 3 4...n
y=11 8 5 2...?

I think it's a linear relation but don't know the equation that goes with it.

Linear systems 2009-02-20
From Rose:
I have been having trouble trying to figure out these three math problems , I need help breaking them down so I could understand them better please help.
1. x = 7 - x
2 x - y + 8

2. 8 x + 5 y = 1 8 4
x - y = 3

3. y + 2 x = 3
y + 2 x = 4

I can't figure out how to break them down in the right order.

The substitution method 2009-02-18
From Nicolette:
I am working on linear programming problems that I need to solve pairs of linear equations for. I am confused and am not sure how to solve these problems!
5x+3y=7      y=x-3 How can i solve this using the substitution method?

A line parallel to a given line 2009-02-18
From Lisa:
I'm having a hard time understanding the concept of how to write an equation of the line containing the given points and parallel to the given line.
Express the answer in the form of y=mx+b. (7,9); 2x+5y=4. i would appreciate it alot if someone can show ne how to do this. Thank you, Lisa

Solving an equality 2009-02-10
From Deborah:
2(v+10)<18
Linear speed 2009-01-26
From Hom:
A semi is driving cross country at 70mph. The tires on the semi have a 3 foot diameter. What is the linear speed in feet per minute?
Using y = mx + b 2009-01-26
From Caroline:
How do you write a symbolic representation using the y=mx+b method?
Solve for x 2009-01-16
From maritza:
5=3(x-2)=
0.0708 lbs per linear yard 2009-01-16
From Kevin:
If I know that my product is .0708lbs per linear yard how do I calculate how many Linear yards are in a lb?
The table of values for y=3x-10 2009-01-09
How can I know the value of x for y=3x-10 in this table of values pls. include the deatails

if x=-2 y=-16
if x=3 y=-1
but how if y=2 what is x

A line in slope intercept form 2008-12-08
From laurie:
the question: Write and equation of the line that passes through the point and has the give slope. Then rewrite the equation in slope intercept form. (2, 5 ) m= 3
Solve 3x +5= 4x-10 2008-11-22
From Nikko:
HELP please how do I solve these type of questions? 3x +5= 4x-10 or 4x +10= 6x-8
A belt drives a pulley 2008-11-03
From Rebecca:
A point on a belt is moving at the rate of 30 ft/sec and the belt drives a pulley at the rate of 200 rpm. What is the radius of the pulley?
A linear system 2008-10-22
From Tiffany:
solve:

x + y + z = 4
2x - 3y - z = 1
4x + y - 2z = 16

Two equations in two unknowns 2008-10-17
From Dushayne:
a. 3x-4y=32
5x+2y=10

b. 2x+3y=11
4x+3y=10

Using the augmented matrix 2008-10-17
From Karlena:
I am supposed to write the augmented matrix of the system and use the matrix method to solve the system. I must show my work algebraically

x+y+2z=30
2x+3y+2z=53
x+2y+3z=47

Linear and Angular Velocity 2008-10-10
From Matthew:
The pedal and gear relationship of a bicycle is shown. The radii of the gears are r(sub1) = 5 cm and r(sub2)= 12 cm. The radius of the wheel is r(sub3) = 30 cm. How many rotations per minute of the pedal gear will produce a racing cyclist's speed of 60 km per hr. For a diagram: http://bikepedalsgears.weebly.com/
A linear equation with fractions 2008-10-07
From Christopher:
1/6(x-18)+1/8(x+8)=x-9
The vertices of a triangle 2008-09-27
From T.:
how do you find the coordinates of the vertices of the triangle with the sides determined by the graphs of the following equations:4x+3y+1=0,4x-3y-17=0,4x-9y+13=0?
Collinear 2008-09-08
From Patrick:
On page 17 of my son's 9th grade math book Geometry by Jurgensen, Brown, and Jurgensen (copyright 2004), the authors state from the diagram that you can conclude the points A, B, and C are collinear. In the diagram, the points A, B, and C appear to be situated on a straight line; however, nothing in the diagram states that it is a straight line. I told him that you can't conclude they are collinear because angle ABC could be 179.9 degrees instead of 180 degrees since nothing in the diagram states otherwise. His teacher marked his answer incorrect on a test but I still believe that I am correct. How do conclude points are collinear if nothing tells you that they are situated on a line?
A word problem with three numbers 2008-09-02
From Wanda:
"Jabari is thinking of three numbers. The greatest number is twice as big as the least number. The middle number is three more than the least number. The sum of the three numbers is 75. Find the numbers."
Angular & Linear Speed from a Sine Graph 2008-08-19
From Kim:
Kim, a student: I am given a graph with a wave. The amplitude is 5cm and the period is 4cm. I am suppose to find the angular speed. What I need to know is the formula for angular speed and how do I use these numbers to get the correct answer.
A linear function 2008-08-07
From Warren:
What are the conditions of the numerical coefficients of the standard form Ax+By=C in Linear Function? How will you transform y=square root of 3 x + 1 in standard form Ax+By=C?
Two equations in two unknowns 2008-08-01
From James:
Question from james, a student:

3x+2y=9;24x-2y=18

My math teacher says that it is (2,-4)

Can someone please explain how to figure this out by graphing?

Simultaneous equations 2008-07-23
From Franco:
Solve

3 D + E - F = -10
-2 D - F = -4
-3 D - 4 E - F = -25

Franco

A rectangular room 2008-06-30
From Peter:
A rectangular room has a perimeter of 42 feet and an area of 108 square feet. What is the length, in feet, of the shorter side?
Substitution method 2008-05-30
From taquicia:
2y-x=3
x=5+y

x/4 = 3 1/2 2008-05-30
From Kelsey:
How do you solve for "X" in the problem below?

X
--- = 3 1/2
4

--Kelsey

How old are the sisters? 2008-05-11
From George:
Theresa is four years older than her younger sister Joni. Twelve years ago, she was twice as old as her sister. Find the present age of the two siblings.
A linear model 2008-05-09
From Shelby:
How would you write a linear model to represent the population of a city that has a population of 547,725 and a growth rate of -25,195 per year with t represents the number of years since 1994?
15 + 0.10n = 0.25n, solve for n 2008-04-24
From monica:
15 + 0.10n = 0.25n

Solve for n.

x/3 -5 = 3(x-2) 2008-04-20
From Mrs:
I am having trouble helping my son solve the following equation:

x/3 -5 = 3(x-2)

A linear system 2008-03-10
From sandhiya:
one group of people purchased 10 hotdogs and 5 soft drinks at a cost of \$12.50. a second group bought 7 hotdogs and 4 soft drinks a ta cost of \$9.00 find the cost of a single hot and a single soft drink.(using the row echelon form to solve)
Simultaneous equations 2008-02-29
From CONOR:
I was wondering if you could help me with this problem

7x - 5y = -1
3y = 4x

A inear system 2008-02-03
From Kelly:
is (-1,5) a solution of each system? y=-x+4 y=-1/5x
Two equations in x and y 2008-02-01
From leslie:
6x+8y=40 4x+5y=25
Linear feet to metres 2008-01-25
From Jillian:
i have a measurement of something in linear feet. i dont know what a linear foot is so i want to convert it to meters to have an idea. how do i convert.
A linear system 2008-01-22
From Lisa:
I am supposed to use augmented matrices to solve this system of equations. x - 3y = 5; 4x - 12y = 13. I think it is unsolvable but I want to be sure I am not just giving up. Thanks in advance for your help! Lisa.
Answered by Stephen La Rocque and Brennan Yaremko.
How many rolls of stock do I need to buy? 2008-01-16
From Dan:
How many rolls of stock do I need to buy?
Given:
The rolls are 40" wide, 20" roll o.d., 4" core o.d., gauge is 0.008" I need to cut these master rolls in 6" strips (4" of waste per master roll) and I need 1,270,500 linear feet of this strip.

Linear systems 2008-01-10
From Sandra:
I have two questions. Please solve both. Thank you.

1.) In your chemistry class, you have a bottle of 5% boric acid solution and a bottle of 2% boric acid solution. You need 60 milliliters of a 3% boric acid for an experiment. How much of each solution do you need to mix them together?

2.) You plant a 14-inch hemlock tree in your backyard that grows at a rate of 4 inches per year and an 8 inch blue spruce that grows at a rate of 6 inches per year. In how many years after you plant the trees will the trees be the same height? How tall will each tree be? Thank you. I did not understand neither problem, so I could not show any work. Please help.

Answered by Stephen La Rocque and Harley Weston.
Donuts and bagels for the first period class 2008-01-08
From Karen:
Mr. Pace bought breakfast for his first period class. Ten donuts and fifteen bagels cost a total of \$15.75. Mrs. Pace bought breakfast for her class. Five donuts and twenty bagels cost a total of \$17.00. Set up and solve a system of linear equations to determine the cost of one donut and one bagel.
What is the speed of the plane in still air? 2008-01-05
From oscar:
A plane flies 400 miles with the wind and 340 miles against the wind in the same length of time. If the speed of the wind is 24mph, what is the speed of the plane in still air?
Linearize a graph 2007-12-19
From Justene:
My daughter has a physics lab where she must linearize a graph of acc vs. mass. I have no idea how to help her.
An augmented matrix 2007-11-29
From Beth:
I am having troubles fiinding this augnmented matrix. I know how to do it but everytime i do it it get a different answer and its not the right answer. Could you help me to make sure I do it right?

Here is the problem:
4x - 3y = 5
2x +9y = 6

I have a piece of material 44 inches by 78 inches 2007-11-02
From Marianne:
I have a piece of material 44 inches by 78 inches. How many linear yards can I get from it?
collinear points 2007-10-26
From Carl:
the points H,S,D,K,L, and B are collinear.
KS+SB=KB
DH+HS=DS
DH+HK=DK

point L and B are not between any other labeled points on the line.
<------------------------------------------------------------------------->

Domain and range 2007-10-12
From Dawn:
Hi, I've been out of school for 8 years and recently picked up a math correspondence course. I'm having trouble trying to figure out the range and domain of a linear function. I've read everything I can find in my text, lessons and on your site and I still can't figure out what I'm suppose to be doing. The function is y=2x+1. Please help.
Finding equations, intersection point of two lines at right angles 2007-09-22
From Yaz:
Find the equation of the line joining A(-1,-9) to B(6,120). Another line passes through C(7,-5) and meets AB at rigth angle of D. Find the euation of CD and calculate the co-ordinates of D.
Two equations in two unknowns 2007-09-22
From Mary:
Having problems doing this problem, looking for a solution with the work. I would like to see how you got your answer, to see what I was doing wrong.

solve using the substitution method, is there "no solution" or "infinitely many solutions"

4x+y=4
2x+8y=0

Answered by Stephen La Rocque and Leeanne Boehm.
A nonlinear system 2007-08-14
From Marsia:
Explain how the solution of a nonlinear system could be just a point, or two points. Sketching these may make it easier
Linear systems and inverses 2007-08-06
From Marsia:
explain how inverses are used to solve linear systems.
A linear system 2007-06-29
From Kim:
solve for x,y,z

x-y+z=4 2x+2y-z=-2 x-2y+2z=7

The substitution method 2007-06-23
From mary:
solve the system by the method of substitution: -5x+2y=-15 4x-y=9
Factor X^6 - 64 2007-06-20
From Krystal:
How do I Factor X^6 - 64 into linear factors?
A system of linear equations 2007-06-14
From Alfredo:
A student club sponsored a jazz concert and charged \$3 admission for students, \$5 for faculty, and \$8 for the general public. The total ticket sales amounted to \$2542. Three times as many students bought tickets as faculty. The general public bought twice as many tickets as did the students. Set up the equations that determine how many tickets were sold to each group and solve.
Answered by Stephen La Rocque and Penny Nom.
What happens when you have zero's on both sides? 2007-06-05
From Lily:
On the substitution method what happens when you have zero's on both sides of the equation? Is that considered no solution or infinitely many?
Answered by Stephen La Rocque and Penny Nom.
Linear growth 2007-05-11
From Rebecca:
What is the definition of linear growth?
The substitution method 2007-05-08
From A student:
I need help on these two problems( substitution method)

-2x+7y=10
x-3y= -3
and
6x-8y= -12
-3x+4y=9

The vertices of a triangle 2007-05-02
From natakie:
Find the coordinate of the vertices of a triangle whose sides lie on the following three lines. 2x+5y-16=0, 4x-3y-6=0 and 3x+y+2=0
Two equations 2007-04-29
From lavon:
I'm having trouble figuring out a linear equation, can you help?

- 3x + 2y = 8
3x + 2y = 8

Finding out if two line equations are parallel or perpendicular 2007-04-28
From Vincent:
Can you determine if the two lines are parallel, perpendicular, or neither 1/2x+4y=3/5 y/1 + 10/5= 8x I think there perpendicular but how would you solve the equations
A linear system 2007-04-25
From Tee:
2x -y =5
2x +=y =5

and also
3/7x + 5/9y =27 (fractions)

I have to find the addition method to both problems

Linear programming 2007-04-24
From Sylvia:
What is graphing linear programming?
From Hector:
y=x^2-4x+3
y=x-1

No solution to a linear system 2007-04-09
From Ryan:
When is it possible to get no solution when solving a linear system?
Answered by Leeanne Boehm, Steve La Rocque, Penny Nom and Melanie Tyrer.
Solve for x and y 2007-03-27
From anthony:
solve y=4x and x+y=5
A linear system 2007-03-23
Solve the system by graphing:
4y>6x
-3x+2y<-6

Answered by Stephen La Rocque and Penny Nom.
Simultaneous equations with fractions 2007-02-28
From Alyca:
Hello Math Central, I am a grade 10 student taking Academic math. Our unit right now is method of substitution and elimination. I'm stuck on this one question that I've been doing forever. Please help =)

*For this equation I have to do method of elimination, but it's so much harder with fractions...could some one please explain to me how to do it step by step?*
x y 2
-- - -- = - --
3 6 3

x y 1
-- - -- = 1---
12 4 2

Answered by Steve La Rocque and Ashley Mang.
An augmented matrix 2007-02-13
From Mary:
I've been trying for quite some time now to figure this out. I have to solve this by using the Gauss-Jordan Method: 3x - y = 15 2x + 3y = 10 Can anyone help me?
Answered by Penny Nom and Gabriel Potter.
Dividing money unequally 2007-02-06
From Linda:
I have a total of \$13,826.48. It is to be divided by 15 kids - 2 of the kids only get half of what the other 13 do - how much do the 13 get and how much does the 2 get? Thanks
Answered by Haley Ess and Steve La Rocque.
Nickels, dimes and quarters 2007-02-05
From Avinash:
Mary has 48 coins made up of nickels, dimes and quarters with a total value of \$5.10. She has 4 more dimes than nickels and quarters combined. How many coins of each kind does she have? Use matrix to solve the system
Patrick's new job 2007-02-02
From kathy:
patrick has been offered jobs by two different automobile repair shops. his income from the first shop will be \$1,200 per month plus 3% of the monthly sales. the second shop will pay patrick \$1,500 per month plus 2% of the monthly sales. part a let s equal the amount of monthly sales and i equal patrick's income in dollars. write a system of two equations that could be used to determine the monthly income from either shop. part b solve the equation to determine what amount of monthly sales for each shop would result in patrick earning the same monthly income, i, from both shops
The substitution method 2007-01-31
From Victoria:
how do i solve this problem using the substitution method?
2x-5= -14
-7x+14y= -5

The elimination method 2007-01-31
x-2y=2
3x-5y=7

A boat travels 60 miles downstream in the same time it takes to go 36 miles upstream 2007-01-27
From Liz:
A boat travels 60 miles downstream in the same time it takes to go 36 miles upstream. The speed of the boat in still water is 15 mi/h greater than the speed of the current. Find the speed of the current.
The sum of the digits of a two-digit number is 13. 2007-01-27
From Liz:
The sum of the digits of a two-digit number is 13. If the digits are reversed, the new number is 9 more than the original number. Find the original number.
An algebra exercise 2007-01-24
From Clara:
Given x + 2y = -2 and x - 2y = 18, find:
a) x^2 - 4y^2
b) x^2 + 4y^2

Answered by Stephen La Rocque and Penny Nom.
Points of intersection 2007-01-18
From Mark:
Find the points of intersection of the given pair of curves. 2x - 3y = -8 and 3x - 5y = -13
Answered by Steve La Rocque and Haley Ess.
x + 2y < 6 2007-01-06
From Mike:
I understand solving by graphing, but i am having trouble with the graphing of in equalities. i solved : x + 2y<6
A linear system 2007-01-04
From Harold:
System A (4, 2/3)
2x-3y=6 and x-3y=2

I approached this problem using the addition method.

Could i have found the answer using the graphing method?

Linear inequalities 2006-12-01
From Susan:
how would I graph a linear inequality of y>3.
How high is the satellite above the earth? 2006-11-13
From Naomi:
If the linear speed of a satellite in synchronous orbit is 1000 mi/h, how high is the satellite above the earth?
Solving a linear equation 2006-10-12
From Eriona:
6p-5=17. I have to solve the equation.
Plotting a linear equation 2006-10-09
From Jennifer:

I am having problems explaining how to do these problems to my child .

graph:2=x-y

graph the equation: 2y+x=-3

Linear systems 2006-09-21
From Alexander:
Hello, i have a math assignment due tonight at midnight and i need some help please

It is using the addition method to solve linear systems

Convert a standard form to a slope intercept form 2006-09-14
From Maiko:
I need to know step by step procedures to convert a standard form to a slope intercept form?
I want to calibrate a glucose meter 2006-07-27
From John:
If I have 3 glucose control solutions having:
Low - 50 mg/dl
Normal - 100 mg/dl
High - 330 mg/dl

I want to calibrate a glucose meter but I need more than these 3 data points. How can I mix these up to get different concentrations in between 50 and 100, 100 and 330. I would like to mix up different concentrations and put them in test tubes or whatever to do some calibration work. Like 70 mg/dl, 90 mg/dl, etc. More data points should be in between say 50 and 100 since this is normal, 90 mg/dl is considered close to normal.

How old is y = mx + b? 2006-07-05
From Beckie:
I am taking intermediate algebra this summer (Math 95), and have a question for you. My instructor will award extra credit points to any of us who find out how old the formula y = mx+b is. Would you happen to know the answer?
Square feet and linear feet 2006-06-10
From Richard:
Need to know how many linear ft are in 2800 sq.ft
Three people go to a store where there is a sale 2006-05-30
From Geocee:
Three people go to a store where there is a sale. One person buys two shirts, one pair of pants and one sweater. The second person buys one shirt, two pairs of pants and two sweaters. The third person buys three shirts and four pairs of pants. Find the price of each item if the first person spent \$155 and the second and third person spent \$235 each.
Absolute Value vs. Standard Deviation ? 2006-04-24
From Sonia:
Why we don't just take the average of the absolute value of difference scores (use the mean deviation) to describe variability instead of calculating the standard deviation?
Finding the inverse of a function 2006-04-12
From Sam:
If g(x) = 2x+3/5 then how do I find the inverse?
x-7=20 and 2x+5=17 2006-04-04
From Janette:
I'm trying to help out my daughter, it has been much too long since I've been in school. The question is x-7=20 and the other question is 2x+5=17. What are the formulas?
2x+5y=3 And -x+3y=-7 2006-04-03
From Lloyd:
simplify 2x+5y=3 And -x+3y=-7
Angular velocity 2006-03-28
From Ben:
How do you (a) express angular speed in terms of linear speed and (b) express linear speed in terms of angular speed?
Linear feet on a paper roll 2006-03-20
From Vishal:
I WOULD WISH TO KNOW OF A STANDARD FORMULA BY WHICH I CAN CALCULATE THE LINEAR FEET OF A PAPER ROLL AS PER THE FOLLOWING DETAILS:-

THICKNESS: 150 GSM (GRAMS PER SQUARE METER)
REEL WIDTH: 85 CM
REEL DIAMETER: 140 CM
REEL INNER CORE: 10 CM
REEL WEIGHT: 946 KG's

2x+3y=0 and 3x-y=0 2006-03-14
From Lisa:
my name is lisa I am doing math for work and i have a math problem to solve and i need help with it here is the question 2x+3y=0 and 3x-y=0 this is one question can you help me please
The graph of y = 2x + 1 2006-02-23
From Geneva:
I'm having trouble with graphing equations like y=2x+1 which is my homework I'm not sure how to graph it. I'm in the 8th grade taking a 9th grade course algebra I.
One boundary of a pond is parabolic in shape. 2006-01-20
From Glenn:
One boundary of a pond is parabolic in shape. The boundary passes through the points A(-20,45), B(40,40) and E(30,35). The equation of the parabola is of the form y=ax2+bx+c. Find the equation of the parabola and the coordinates of the vertex of the parabola. Any assistance you could provide would be greatly appreciated.
Intercepts and slope 2006-01-15
From Anthony:
Given -1.7x + 0.8y=7.1:

(a) state the intercepts and slope for the graph

(b) Draw the graph

y - y1 = m(x - x1) 2006-01-08
From Greg:
How do you change 2x + 3y = 7 into y - y1 = m(x-x1)?
Simultaneous Equations 2005-12-21
From Matt:
I have these two equations,
336 = 60a + 10b
and
432 = 84a + 6b
Am I right in saying both a and b are 4.8?

5(x-3)/4 =x+1 2005-12-14
From Jennifer:

I have two problems i am stumped on I don't know how to help my daughter.

5(x-3)/4 =x+1
3(x+12)/5 =x +2

2/n +4 = 10- 4/3n 2005-12-11
From Jennifer:

2/n +4 = 10- 4/3n

5(x-3/4) = x+1

Solve for x 2005-12-04
From Lisa:
5(x-4)=3(2-3x)
Express t as a function of d 2005-11-30
From Matthew:

I have a problem on my homework I cant seem to figure out. Basically it gives me this Linear Regression Equation:

ln t=1.5 ln d-0.8954

and it wants be to transform the equation expressing t as a function of d. For some reason I keep getting it wrong. Anyone got an idea of how to do this?

Graphing two lines 2005-11-20
From A student:
About y = 5x + 24 and y = -3x - 8
1. Graph both equations on the same set of axes. When you made your graph, how did you choose the range of x and y values?

2.Find the point of intersection for the graphs.

3. Test the point of intersection you found by substituting its coordinates into the equations. Do the coordinates fit the equations exactly?

Solving a pair of equations 2005-11-10
From Steven:
2 x + y = 1
y = -1/3 x - 4

What is the angle between 2 non-collinear parallel lines? 2005-10-17
From Ben:
What is the angle (if any) between 2 non-collinear parallel lines?
Answered by Chris Fisher and Walter Whiteley.
2x - 5x + 6.3 = -14.4 2005-10-16
From Leslie:
How do we solve 2x - 5x + 6.3 = -14.4
A piecewise function 2005-09-15
From Duncan:
A child is assigned to your care and she has a headache. The parent has authorized the administration of Children's Tylenol. Read a box of Children's Tylenol (or any other similar drug) and find the directions for administration. Note the child's weight and the corresponding dosage. (Be sure the drug you choose has a minimum of 4 weight intervals.)
Graphing a linear inequality 2005-08-26
From Gina:
When graphing a linear inequality, how do you know if the inequality represents the area above the line?
Labour efficiency 2005-08-23
From Rob:

The problem, on the surface, seems very simple and yet has created some controversy among a group of accountants. The problem itself has to do with labour efficiency rates and only involves two variables; standard working hours, and actual working hours. The difficulty lies in deriving an efficiency % from these two numbers.

Standard working hours or the targeted number of labour hours required to produce one widget, which I will represent as "s". Actual working hour or the actual number of labour hours require to produce one widget, which I will represent as "a". Labour efficiency I will represent with "E". The prevailing calculation with which I have a problem with is this:

s/a=E or if s=3000, and a=4000 then 3000/4000=75%

What bothers me about the calculation is that the standard hours get represented as a percentage of the actual hours and in my opinion changes the focus of the calculation from standard or target, where it should be, to the actual hours. I cannot define why, but this just seems inherently wrong to me.
The calculation that I use:

(1+((s-a)/s))=E or if s=3000, and a=4000 then (1+((3000-4000)/3000))=66.67%

My calculation is like a %change from standard calculation. However, there is something that also concerns me about my calculation.

If you substitute 100 for a and 50 for s, then you come to a quandary, because if you plug those numbers into the second equation the result is of course zero % efficient which doesn't sit right with me either. If you plug them into the first calculation you get 50% efficiency which doesn't really seem to work either, because you require 100% more hours to do the same work in this case. ???

Is the first calculation correct? Am I missing something altogether? Are both calculations off base?

The substitution method 2005-06-28
how do i know where to began the substitution method? how do i solve y = x + 1 2x - y = 1
An ODE 2004-11-10
From David:
I have a question that i really cant do, it is as follows:

The ODE dy/dx + 0.5y = 0.5e^(-1.5x) ; y(5) = 2

Solve the ODE subject to the given condition using exact methods and evaluate the solution y for x = 5 x=5.2 x=5.4 x=5.6 x=5.8 x=6

Pizza for Jack? 2004-09-16
From Grace:
Jack is playing pool with Jim for \$1 a game. He has only \$2 and decides to play until he goes broke or has \$5, at which point he will quit and go out for a pizza with Jim(Dutch treat). Jack knows from past experience that he beats Jim 60% of the time. What is the probability that Jack will get to eat pizza? Hints: Let A be the 6x6 matrix defined by A=[aij], where aij is the probability that Jack will have \$(i-1)after one game is he starts with \$(j-1). For example, a23 - .40 since there is a 40% probability that Jack will end up with \$1 after a game is he starts the game with \$2 (If Jack wins 605 of the time, he must lose 40% of the time). Also, for example, a52 = 0 since there is no way jack can have \$4 after one game if he had \$1 at the beginning of the game. Since Jack will stop if he goes broke or accumulates \$5, a11 and a66 are both 1.

Let x0 = [0 0 1 0 0 0 ] transposed, which we interpret as saying that initially Jack has \$2 with a probability 1. Then Ax0 will represent the porbability of each amount of money, \$0-\$5, after one game. What is the probability that Jack will be able to eat pizza by computing Akx0 for large k and finding a limiting value.

Solving an equation 2004-06-14
From Anthony:
I was hoping that you could help me with this problem. I believe that this is a high school level problem but as an adult who has forgotten the "rules", I am stuck.

the equation is this: x=t2/(t1-t2)

we know that x=5.73
t1=303

we must solve for t2

Solving an equation 2004-01-03
From A student:
the question is to solve and check equations and the question is
2n + 3n + 7 = -41

Making a windmill 2004-01-02
From Matthew:
I am a farmer in Ontario. It has been almost 20 years since high school. I am toying with making a windmill. The output chart for the the old generator I have is shown below. Before I tear it appart I would like to develop a formula from the chart that can predict the output at various speeds.
Mr.Carter is very cautious 2003-11-26
From Bob:
Mr.Carter is very cautious. He decides to invest in only three stocks: one low stock, one high stock, one medium stock. Given that the expected annual yields are 6% for low stock, 7% for medium stock, and 8% for high stock, he wants his investment in medium stock to be half of his total investment in low and high stock. How much should I invest in each type fo stocks to expect a total annual return fo \$650 form my investments?
The substitution method 2003-04-14
From Patty:

I need help with the following:

5x - 4y = 13

2y + 3x = -1

Two investments 2003-02-07
From A student:
you have \$7200 in principal and invest different sums @ 10% and 14%. You receive 920 at end of term. (one year)What amounts are invested at what rate?
Two equations in two unknowns 2003-02-06
From Patrick:
What are all ordered pairs of real numbers (x, y) for which: yx2 - 7x + 12 = 1 and x + y = 6?
Collinear Points 2003-01-13
From Gary:

Which of the 4 points are collinear when you construct the following concurrent lines or rays of a triangle?

1. P(1), the point where the angle bisectors intersect.
2. P(2), the point where the altitudes (or extensions) intersect (inside or outside of the triangle).
3. P(3), the point where the medians intersect.
4. P(4), the point where the perpendicular bisectors (or extensions) of the three sides of a triangle intersect.

This is for my 9-12 high school class in geometry.
My name is Gary

Gary

Answered by Harley Weston and Chris Fisher.
The intersection of conics 2002-12-19
From Glenda:
We are studying systems of equations where two conic sections are the two equations that we are solving simultaneously. We were studying the number of solutions that are possible if you have an ellipse and a parabola. We all agree that there can be none, one, two, three or four solutions. The question that the students had for me was whether or not a portion of an ellipse and a parabola can overlap and thereby allow an infinite number of solutions. What should I tell them?
Answered by Chris Fisher and Harley Weston.
x + y=80 and x + z=100 2002-11-28
From PJ:
x + y=80
x + z=100

can you solve for x, y or z?

A two stage rocket 2002-11-26
From Hoda:
a two stage rocket accelerates in free space by ejecting fuel at a constant relative speed , v(ex). the full fuel load makes up 80% of the initial mass of the entire two stage rocket . the rocket accelerates from rest until at the end of the first stage when 75% of its fuel has been burnt. find an expression for the speed of the rocket at the end of the first stage in terms of v(ex).
Performance reviews 2002-11-21
From Lara:
Perhaps you can help.

He's doing performance reviews at work.

The average performance review is 3.92 on a 5.0 scale. This person would receive a 3.5% raise for next year.

The highest performance review is 4.9 and this person would recieve a 6.0% raise for next year.

How do I solve for the other performance review numbers.

The substitution method 2002-11-15
From A student:
Solve by using the substitution method.

x = 3y - 1
x + 2y = 9

Determining a parabola 2002-11-06
From Shelley:
let (0,3) and (1,9)and (-1,1) be given points in a parablola. Determine a b and c
A linear function 2002-09-09
If y = 9x - 13 does it represent a linear function? And if it does what is its slope and is it a direct variation?
Two equations 2002-07-26
From Derek:
1. 3x + 2y = 4
2. -7x + 2y = 24

finding x and y.

Linear programming 2002-05-27
From Jes:
A machine shop makes two parts, I and II, each requiring the use of three machines, A, B, C. Each Part I requires 4 minutes on Machine A, four minutes on Machine B and five minutes on machine C. Each Part II requires five minutes on Machine A, one minutes on Machine B and six minutes on Machine C. The shop makes a profit of \$8 on each Part I and \$5 on each Part II. However, the number of units of Part II produced must not be less than half the number of Part I. Also each day the shop has only 120 minutes of machine A, 72 minutes of Machine B, and 180 minutes of Machine C available for the production of the two parts. What should be the daily production of each part to maximize the shop's profit?
25m = 100 2002-04-22
From Megan:
If 25m = 100, Then m equals what number?
An augmented matrix 2002-04-20
From A student:
Hi my math teacher asked us to solve an augmented matrix. I am in twelfth grade and need help. The book we are working on is college algebra. Here it is

a+2b+c=0
2a+5b+4c=-1
a-b-9c=-5

3/4n-6=12 2002-04-07
From Diane:
I am in 6th grade advanced math and I just started Algebra. My teacher tries to explain it to me but I just can't get it. I am having difficulty understanding it. Please HELP!!! I will type a problem, if you could answer it and show your work so i can understand it that

would be great. Please explain in simple terms.

here is a couple problems I am having trouble with,

PROBLEM #1

3/4n-6=12

Pairs of equations 2002-04-04
From A student:

high school level

```y=4x x=-4y
x+y=5 3x+2y=20

y=x-1 3x-y=4
x+y=3 2x-3y=-9

x+5y=4
3x+15y=-1

. . .
```

If the matrix A is inverible and AB =AC, then B = C 2002-03-27
From Vikki:
i hope you can help i am soooo stuck here goes:

a)

` A= 0 1 B= 1 1 c= 2 5    0 2    3 4    3 4 `
A,B and c are matrices

Evaluate AB and Ac (which I can do)

then

b)
I need to prove that if the matrix A is inverible and AB =AC, then B = C. Why does this not contradict what happened in part a)?

The substitution method 2002-02-24
From Joe:
whats the answer to this question? 3x+y=11
x+2y=-3

its substitution method i am having alot of trouble figuring it out. send the answer as soon as possible. thank you

Linear regression 2002-01-16
From Murray:
If you have a set of coordinates (x[1],y[1]),(x[2],y[2]),...,(x[n],y[n]),find the value of m and b for which SIGMA[from 1 to m=n]AbsoluteValue(y[m]-m*x[m]-b) is at its absolute minimum.
Algebra review questions 2002-01-14
From A student:
1. A wildebeast was observed racing a distance of 86.4m in 4.8 seconds. Find the speed of the wildebeast in m/s.

2. 8x - 7 - 5x = 23

3. 7 z - 3 (z + 2) = 26

Simultaneous equations 2001-12-17
From Matthew:
4x + y = 4
2x - 3y = 5

what is x and y

y = zx - x - c 2001-12-11
From Andrew:
Could you please help me work out the value of x where: y = zx - x - c
Two equations in two unknowns 2001-12-04
From Courtney:
y = 3x + 2
y = 4x - 5

solve for x

Slope intercept form 2001-11-27
From A student:
what is slope intercept form?
Matrix 2001-11-21
From Hoda:
I have a question about matrix multiplication; well, actually, matrix division. I am assuming that matrices are divided the same as they are multiplied; that is, row by column. But what happens if you have to divide by zero? How does this affect the resulting matrix?
Answered by Patrick Maidorn and Penny Nom.
3x-1/2(x-4)+5= -3 2001-11-13
From Tausa:
3x-1/2(x-4)+5= -3
A linear inequality 2001-09-17
From Eric:
How can I solve |x + y| + |x - y|< =6?
Linear regression 2001-08-01
From A student and a mother:
My mom is taking a correspondence course in Simple Linear Regression and Correlation Analysis and we've been arguing about the relationship between the correlation -rxy and standard estimate of error-Sy.x. I took statistics last year in high school and I remember something about the Sy.x being proportionate to the r. Are they inversely related, directly related, not related, or can only range from 0 to 1.00? Her book doesn't say very much and I believe they are inversely related. She says they're directly related.
Answered by Chris Fisher and Penny Nom.
The best linear model 2001-07-29
From Rebeca:
I am a student (senior) summer hire working for Dept of the Army Resource Management. I've been assisting the Analyst in developing a model to predict training costs. The technique we used was simple linear regression. Now I've been asked for my opinion in choosing the best model I feel is better. I've chosen #1. Garrison Training but I want a second opinion before I give my choice. I've taken basic statistics last year in high school and will probably be taking more this year. Could you look over the information and give me a reason my choice would not be best? The dep variable-y, is Training costs in dolars per day.

ModelInd Variable- Xabrsy.x
1.Garrison Training126.310.9820.9055117.2
2.Local Training212.161.370.7937142.7
3.Man Rig Area116.382.470.6481175.6
4.Major Training346.124.670.7280167.2

Matrix reconstruction 2001-07-19
From Guy:
Is there a way to get the sums of rows, columns and diagonals of an n x n matrix to reconstruct the original matrix?
Answered by Walter Whiteley and Patrick Maidorn.
Common solution 2001-06-02
From Samantha:
1. Solve for common solution: x+y=6 2x-3y=2

2. Solve for y in terms of x: 3x-y=4

Solving some equations 2001-04-16
From Justin:
Solve the following equations for x
1. x+7=10
x=

2. x-7=10
x=

3. 3x=7
x=

4. x/3=10
x=

5. .

6. .

7. .

8. .

Where do the lines y=2x-4 and y=x-1 intesect? 2001-04-06
From Bryce:
solve the following problem by setting them equal to each other. Solve for x and y. Where do the lines y=2x-4 and y=x-1 intesect?
Matrices 2001-03-26
From Peg:
What are some applications of matrices, basic trigonometry, and linear systems in the real world? I'm writing and Algebra report about where these topics are used outside of the classroom.
Answered by Judi McDonald and Walter Whiteley.
Systems of equations 2001-03-16
From joy:
How do u solve problems using systems of equations?
~ finding x and y~

ex:

26 = 3x - 2y
42 = 4x + y

The substitution method 2001-03-05
From A student:
Solve each system of equations by the substitution method. Show your work.
1. y = 8
7x = 1 - y

2. y = x - 1
4x - y = 19

Solving Equations 2001-02-23
From Stephanie:
Do you know who came up with solving equations?
Do you have any web-sites that can give me good information on solving equations?
Do you know any history on solving equations?
Do you know what solving equations is used for?
And finally............Sorry about all of the questions :)
Has the form of solving equations changed from the time it came out to now?

Linear equations 2001-02-13
From Jamie:
I have a question how do you do linear equation?
Vitamins A and B 2001-01-14
From Sara:
A diet is to include at least 140 mg of Vitamin A and at least 145 mg of vitamin B. these requirements are to be obtained from two types of food. type X contains 10 mg of vitamin A and 20 mg of vitamin B per pound. Type Y contains 30 mg of vitamin A and 15 mg of vitamin B per pound. if type X food costs \$12 and Type Y \$8 per pound, how many pounds of each type of food should be purchased to satisfy the requirements at the minimum cost?
Answered by Claude Tardif and Harley Weston.
Blood flow and age 2001-01-11
From Gayle:
I don't understand the second part of this problem Here is the first part that was correct. A 35yr old has 100% blood flow. A 65yr old has 64% blood flow. Find the rate of change per yr in the percent of blood flow. (This part is correct) m=(64-100)/(35-65)= -36/30= -1.2 per year of blood flow.

Now, here is the second part I DON'T UNDERSTAND! .Let b represent the percent of blood flow and a represent a person's age. Write an equation that you could use to predict the percent of blood flow for a person of any age over 35.

Networks of satellites and linear spaces 2000-12-08
From David:
Let us suppose some companies have collaborated to place several satellites in orbit. Let us call the set of all satellites that a given company helped place in orbit a network. Finally let us assume the following 4 rules.
1. There are at least two distinct satellites.

2. For each pair of satellites there is exactly one network containing them.

3. Each network contains at least two distinct satellites.

4. For each network, there is a satellite not in it.

What is the least number of satellites.

what is the least number of networks?

A piecewise linear equation 2000-11-24
From Jacky:
There is a light bulb and it is given that the light bulb cost \$0.75 and the cost of operating it is \$0.0081 per hour. From the information give, I came up with the linear equation: Let c be total cost and Let h be hours used. Therefore: c = 0.0081h + 0.75 represents the total cost of the light bulb and the electricity. However, the second part of the question added the fact that the light bulb will only last for 800 hours. If the light bulb is replaced as soon as it burns out exactly after every 800 hours, how can I write an equation that represents that? Is it possible? What would it look like on the graph.
Solving an equation 2000-11-14
From Heather:
4x-3 = 3x+4 these kinds of problems i dont get but everything else in my math class i have got. i just dont understand it.
Connecting to a water line 2000-10-20
From Vanja:
My question is...A house is to be connected to a new water main that runs along the line y=2/3x-1. The connection point at the house has coordinates (2,9), where the units represent metres. What lenght of plastic pipe is needed to connect to the water main at the closest point?
Pillows and Cushions 2000-09-27
From Fiona:

The following problem was given to grade eleven algebra students as a homework assignment. To manufacture cushions and pillows, a firm uses two machines A and B. The time required on each machine is shown. Machine A is available for one full shift of 9.6 hours. Machine B is available for parts of two shifts for a total of 10.5 hours each day.

From Travis:
An art teacher buys exactly 100 items at this sale, and the total cost before tax is \$100. She buys at least one of each item. How many of each item does she buy?

Markers \$0.50
Paint Sets \$10.00

Two linear equations 2000-09-14
From David Dean:
2a + 1b = 3.39 3a + 3b = 6.59
What formula do I use to find what a = ?

How many planes contain a line and a point? 2000-08-30
From Harold:
How many planes contain each line and point?
Slope 2000-08-19
From John K. DePonte:
My question is to why the variable "m" was chosen to represent the slope of a linear equation. I always told my class to think of "m" for "m"ountain slope. But what is the real reason for this?
Two linear systems 2000-08-01
From A student:
hint: let a = 1/x and b = 1/y substitute these expressions into the system to find a and b. Then find x and y.

This is a question I answered wrong on a test: solve the given system for x, y, and z. Express your solutions in terms of a, b, and c.

The equation of a parabola 2000-05-22
From Ian Forsyth:
Given the points A(0,0) B(60,10) C(24,d) find the equation of the parabola. leave the equation in terms of x, y and d if the general form of a quadratic is y = ax2 + bx + c.
Graphing a linear function 2000-05-17
From Chelsea:
I need help with grahing linear functions.If you could e-mail me back the basics and how tos I would be much appriciative.
A matrix equation 2000-05-14
From A student:
Right now, we are dealing with matrices and we are supposed to solve the following problem on our graphing-calculators: 2a+3b-4c+d=20
a-2b+3c-5d=-14
3a+4b-2c+3d=19
5a-b+6c+4d=-5

Taxis in Chicago 2000-03-27
From A high school student high school student:
Suppose that taxis pick up and deliver passengers in Chicago, which is divided into three zones. Records kept by the drivers show that of the passengers picked up in Zone 1, 50% are taken to a destination in Zone 1, 40% to Zone 2, and 10% to Zone 3. OF the passengers picked up in Zone 2, 40% go to Zone 1, 30% to Zone 2, and 30% to Zone 3. Of the passengers picked up in Zone 3, 20% go to Zone 1, 60% to Zone 2 and 20% to Zone 3. Suppose that at the beginning of the day, 600 of the taxis are in Zone 1, 100 in Zone 2, and 300 in Zone 3. What is the distribution of taxis in the various zones after all have had two riders?
A system of equations in five unknowns 2000-03-20
From Will:
I have been having some problem with the following question for some time. I would appreciate any help on solving the problem or a solution.

Q: Assume that a system of equations in the unknowns x1, x2, x3, x4 and x5 when converted to row echelon form gives

.
.
.

Systems of linear equations 2000-03-10
From Ann Marie Devereux:
hi there!!, I guess I have a problem!!!
• 3x+4y=10 (over)
4x+y=9

• 2x=5y+3 (over)
x=3y+1

Midpoints and endpoints 2000-02-15
From Jessica Sipes:
I need to know how to find and endpoint using the midpoint and the other endpoint.
Ax + By = C 2000-01-18
From Fatiha Khanboubi:
I was wondering if you could please explain to me how I would write the equation of line through the given points [(4,1), (6,3)] in Ax+By=C form.
Parallel lines 2000-01-12
From Lori:
Find an equation of the line parallel to the given line containing the given point. x + y = 2; (1,2) We know parallel line have the same slope and we know the answer y = -x + 3.
Systems of equations 1999-12-06
From Roger Hornbaker:
I am having problem figuring out x and y solutions.
1. 5x + y = 4
3x - y = 4

2. 3x + 2y = 6
- 3x + y = 0

The elimination method 1999-12-02
From Jennifer:
Could I get an answer to this one:

2x+5y=36
3x+2y=32

I have to use the Elimination method, as I already know how to do Substitution. How do I begin and show my work? I'm attempting to eliminate the values for y.

Linear models 1999-11-09
From Helen Moreno:
What is a linear model?
Why is slope designated m? 1999-08-18
From Peter Komlos:
Why is the slope of a line is designated by the letter "m"?
Graphing a linear equation 1999-05-27
Im in Grade ten and am doing linear equations, I cann't figure out how to make a chart for questions like y = -2x + 3
Parallel and perpendicular lines 1999-04-23
From Crystal Pilling:
My name is Crystal Pilling and I am in 9th grade algebra. We are currently studying parallel and perpendicular lines. I am having trouble with this problem: 3/4x - 5y= 16, (5,-6) I have to find a line that is perpindicular to this line on a graph.

Shopping at Wegman's 1999-04-22
From Stan:
Joanne, Steve, Pat, Alice, Joan, and Bill go to Wegman's at the same time. Joanne buys 2 gal of milk, 1 dozen oranges, 8 apples, and 2 lb. of ground beef, paying a total of \$13.24. Steve buys 3 qts. of milk, 5 lbs. of ground beef, 10 lb. of potatoes, and 2 bags of mixed vegetables, paying a total of \$16.95. Pat buys 3 gal. of milk, 2 dozen oranges, 1 dozen apples, 5 lb. of potatoes, and 5 bags of mixed vegetables, paying a total of \$25.09.
....
Find the cost of: 1 qt. of milk, one orange, one apple one lb. of ground beef, one lb. of potatoes, and one bag of mixed vegetables.

Linear programming and optimization 1999-04-09
From Shams:
What is Linear programming and optimization?
Answered by Jack LeSage and Penny Nom.
Fitting a Curve 1999-01-19
From Kirk:
Hello my name is Kirk from Scarborough, Ontario.

I have been out of a formal education system for thirty years. I program microcontrollers in my spare time. I have built a temperature sensing device ready to go but, thermistors are very non-linear. I do know that there is a way to calculate the input condition of the thermistor and display the correct temperature in degrees C. I am sending a file to show my progression so far.

Linear Equations 1999-01-16
From Casie Tomney:
My dad and I have been trying to figure, how to solve for x on any of these problems my teacher gives us. The problem is:

2h/3 + 1/2 = 5h/6 - 3/4

Thanks!!!!!!!!

Intersection of Planes 1998-12-03
From Lindsay Fear:
My name is Lindsay Fear. I am an OAC student (which is the Ontario equivalent to Grade 12 in most other states and provinces). I am in an Algebra and Geometry course and am currently studying a unit on equations of planes. Our teacher has given us this question that my friend and I have attempted several times, but we are still unable to solve it. My teacher has also suggested using the internet as a resource. The question is:

Prove that a necessary condition that the three planes

` -x + ay + bz = 0 ax -  y + cz = 0 bx + cy -  z = 0 `
have a line in common is that
a^2 + b^2 + c^2 + 2abc = 1

Algebra 1998-11-25
From Casey:
yeah my son brought home a math worksheet and he was wondering and me too if u could help him and me out . he has problems like this 4n+9=7n+2= ??? and he has to show work so if u could help us out that would be great
Linear systems of equations 1998-11-16
From Crystal Girvan:
My name is Crystal Girvan.Im in grade 11. I have a question.We are solving linear systems of equations: comparison method. My questions is. it says

a)use the method of comparison to solve this system a=b-1, 3a+ b=3

b) verify your solutin in a

A Linear System 1998-10-08
From Jason Bussey:
The linear systems with the following pattern all have the same solution. Is their some kind of reasoning as to why this is so?

2x+3y=4
3x+4y=5

4x+5y=6
5x+6y=7

The solution is always x=-1, y=2

Thank you
Jason

Operations Research 1998-10-08
From Lisa Barrett:
What is the history of operations research and the study of linear programming?
Seed Problem 1998-03-26
From Jody A. Johnson:
Seed Problem: The height of an amazing plant grown from a seed varies linearly with the time it has been in the ground. After six days it is 6cm tall and after 60 days it is 15.8m (1580 cm) tall.
1. Write the particular equation giving the height as a function of time.
2. Find the intercepts and explain them.
3. What would be the height in one year?
4. How long would it take for the plant to grow to a height of 1km?

Y-intercept 1998-02-27
From Don Trumpet:
What is the Y-intercept for the problem:Y = -2(x+2) + 9
Intersecting Lines. 1998-02-10
From Erik Heppler:
My typewriter frequently makes mistakes. Suppose I gave you the following system of equations to solve:

35.26X + 14.95Y = 28.35
187.3X + 79.43Y = 83.29

When I looked back, I realized that I meant to use 14.96 as the "Y" coefficient in the first equation instead of 14.95. Solving the system using 14.95 and then solving another system using 14.96 with all other values the same both times results in the intersection points (1776, -4186) and (-770, 1816) respectively.
How can that be?

How many intersections? 1997-10-08
From James:
(a) A collection of eight points, no three collinear. If lines are drawn between each pair of these points, how many points of intersection would there be?