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

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

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

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
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

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?
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)

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

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

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

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
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

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?
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?

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?
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

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
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

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
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.

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

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

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

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

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 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

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.

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

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?
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."
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?
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 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
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.
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?
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

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
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.
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

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

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.
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.
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

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.
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 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

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.
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
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?

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

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
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?
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?

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
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

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

what is x and y

Two equations in two unknowns 2001-12-04
From Courtney:
y = 3x + 2
y = 4x - 5

solve for x

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.
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

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 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