







A system of equations. 
20200427 

From solomon: xy + x =28
x + y +4 Answered by Penny Nom. 





A linear system 
20200402 

From Dadzie: x+s=8→1
y+x=13→2
yp=6→3
s+p=8→4 Answered by Penny Nom. 





A system of inequalities 
20200201 

From Isaac: Austin has x nickels and y dimes, having a maximum of 15 coins worth a minimum of $1 combined. No more than 4 of the coins are nickels and no less than 11 of the coins are dimes. Solve this system of inequalities graphically and determine one possible solution. Answered by Penny Nom. 





Simultaneous equations 
20191016 

From deepak: This is too complicated please help me
8/x  10/y = 1 and x+y=9 Answered by Penny Nom. 





Two power generators 
20190607 

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? Answered by Harley Weston. 





Two linear equations with a fraction 
20190426 

From Asha: 2x=3y …1
x2+4/3(y+1) ...2
note: … is equation Answered by Harley Weston. 





Simultaneous equations with fractions 
20181214 

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 Answered by Penny Nom. 





Simultaneous equations with fractions 
20170909 

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 Answered by Penny Nom. 





Catherine, Molly and Tom 
20170719 

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? Answered by Penny Nom. 





Simultaneous equations with fractions 
20170602 

From Jamal: 1/x + 1/y =5 and 1/y  1/x =1 Answered by Penny Nom. 





Five equations 
20170116 

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 Answered by Penny Nom. 





Simultaneous equations with fractions 
20161221 

From Kimi: I am stuck on this,can someone please help me????
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 Answered by Penny Nom. 





Simultaneous equations 
20161125 

From Rohan: x2/3 + y  1/4 = 13/12
2x/2 + 3 + y/3 = 11/6 Answered by Penny Nom. 





Two equations 
20160917 

From Nilesh: How to solve (xy)^1/2 + 3(xy) = 30 ; xy + 3(xy) = 11? Answered by Penny Nom. 





Two equations with fractions 
20160722 

From kanesh: p/2+q/3=3
p/4+2q/3=3 Answered by Penny Nom. 





Simultaneous equations 
20160625 

From sena: 2x/3+3y/2=1
4x5y=22
simultaneous equation Answered by Penny Nom. 





A pair of equations with fractions 
20160511 

From tiya: hello, i want to know how to solve this question.
m/6+2n/3=6
m/10=2n/5=2 Answered by Penny Nom. 





Solve for x and y 
20160227 

From ntshidi: Y=1/2x+4and1/4x6 Answered by Penny Nom. 





Two equations in two unknowns 
20160213 

From Anumba: 4x + 2y = 4
7x  y = 11 Answered by Penny Nom. 





A system of linear equations 
20160124 

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
xy=9
x+z=12
zn=14
y+n=2 Answered by Penny Nom. 





Two transport companies 
20160106 

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? Answered by Penny Nom. 





Constructing simultaneous linear equations 
20151228 

From Deborah: Linda thinks of a twodigit 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! Answered by Penny Nom. 





Linear equations in two variables 
20151213 

From priya: I have problem in solving these equations please help me today itself very urgent:
I)2x+y=y
II)pie*x+y=9 Answered by Penny Nom. 





A 15 team tournament 
20151028 

From Joseph: We have a 15 team tournament. Each team plays all other teams. We need a schedule were each game has a work team. Thus at each fields we have two teams playing and one working. All teams need to play each other and also be a work team. Any help would be appreciated!! Answered by Victoria West. 





The method of elimination 
20150501 

From oreanna:
Question from oreanna, a student:
How do u solve 2x+9y=3
7x4y=25 in elimination Answered by Penny Nom. 





Two equations with fractions 
20150226 

From Pulane: Hi math centre I've been trying to solve these equations for days now please help
(6/x)(1/y)=4
(9/x)+1=(2/y)
Please help me solve them simultaneously
Thank you Answered by Penny Nom. 





Two equations 
20150216 

From nigel: 2x+1/2y=1
6x3/2y=21 Answered by Penny Nom. 





Math in the universe 
20150121 

From GA: I want to find out examples in universe for this equation:
sin(x)/cos(x)=1 or tan(x)=1. I know the mathematical answer of pie/4 or 45 degree angle.
What I need to know is to find examples of this. I found an example in construction, for example, which is the shape of attic in the house.
I want to find examples in universe like in solar system, in quasars or jets coming out of them, in galaxies, in stars, in black holes, etc
Do you know of any such examples? Answered by Robert Dawson. 





1999 equations in 1999 unknowns 
20141128 

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) Answered by Penny Nom. 





A linear system 
20141014 

From pheter: 4/x  1/y = 3 .... equation (1)
6/x  2/y = 5 .... equation (2) Answered by Penny Nom. 





Two equations in x and y 
20140925 

From seyilogo: solve y=2x  3 and (4x  2y) / x + y = 1 simultaneously Answered by Harley Weston. 





Two equations in two variables 
20140918 

From Susan: (28x + 36y)  [20000  .75(28x + 36y) + 60000] = 5000
x + y = 10000
solving two equations involving variables Answered by Penny Nom. 





The method of elimination 
20140705 

From leo: please explain how can i solve this problem
3x6y=38
6x9y=44
using elimination and simultaneous method thank you :) Answered by Penny Nom. 





Simultaneous equations 
20140620 

From rana: solve the simultaneous equations
a)3x=7y
12y=5x1 Answered by Penny Nom. 





Simultaneous equations with fractions 
20140419 

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 Answered by Penny Nom. 





Base 5 
20130930 

From Zakir: Sir I wanna know something about base 5 number system
Why we use it and who use this ? and what is the purpose of it Answered by Robert Dawson. 





How we convert cm to mm? 
20130908 

From Génesis: How we convert cm to mm? Answered by Penny Nom. 





A system of equations 
20130813 

From Nina: 3x2y=8
x+3y=5
What is the solution of the system of equations Answered by Penny Nom. 





4 linear equations with 3 unknowns 
20130412 

From Marian: how to solve for 3 unknowns in 4 simultaneous equations Answered by Penny Nom. 





Two quadratic equations 
20121122 

From fahmie: graph and solve the intersection of the following equations:
x^2+y^2=4
x^2+2y=4 Answered by Penny Nom. 





Row echelon form 
20120905 

From Jennifer: Hello, my name is Jennifer. I am a 12th grader in PreCalculus 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 Answered by Penny Nom. 





John's electronic store 
20120725 

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? Answered by Penny Nom. 





Four apples and two oranges cost Rs. 30... 
20120113 

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? Answered by Harley Weston. 





Augmented matrix 
20111214 

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
yx=10 Answered by Robert Dawson. 





Linear equations 
20111006 

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 (madeup 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? Answered by Penny Nom. 





What is the speed of each car? 
20101104 

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? Answered by Stephen La Rocque. 





A linear system 
20101015 

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 Answered by Stephen La Rocque. 





x/a +y /b =a+b : x/a^2+ y/b^2 =2 
20100530 

From smithu: x/a +y /b =a+b : x/a2+ y/b2 =2 solve by using elimination method ,
cross multiplication, substitution method Answered by Penny Nom. 





A system of equations 
20100330 

From samantha: the equations of two lines are 6xy=4 and y=4x +2.what is the value of x in the solution for this system of equations? Answered by Penny Nom. 





The sides of a 306090 triangle 
20100329 

From maris: Find the sides of a 306090 triangle whose perimeter is 6. The solution must use systems of equations using 3 variables. Answered by Penny Nom. 





A quadratic equation 
20100315 

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 
Answered by Penny Nom. 





Redwood Park and Glendale Park 
20100305 

From Shaun: Question from Shaun, a student:
Redwood and Glendale Parks are each surrounded by 100 yards of
fencing. The are of Redwood Park is 25 square yards more than the area
of Glendale Park. If both parks are rectangles, what is the measurement
of each rectangle? Answered by Harley Weston. 





How many CDs and videos did the store sell? 
20100301 

From dawn: A used book store started selling CDs and videos. In the first week,the store sold 40 used CDs and videos,at 4.00
per CD and 6.00 per video.The sales for both CDs and videos totaled 180.00 she wrote a system of equations to represent the situation.Then she graph the system of equations
thanks Dawn Answered by Tyler Wood. 





Substitution method 
20100217 

From Melodie: 7x  4y = 10
4y= x2 Answered by Tyler Wood. 





Substitution 
20100214 

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 Answered by Stephen La Rocque. 





A pair of simultaneous equations 
20100109 

From Yumiko: Solve the following pair of simultaneous equations.
x^2 4x = y^24
3y=2x  3 Answered by Penny Nom. 





Solving two equations, one with a square root 
20091123 

From kacie: y = square root of x+3
x4y = 7
im having trouble with this problem...i have to find where they intersect. Answered by Harley Weston. 





A word problem 
20091024 

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! Answered by Penny Nom. 





A linear system 
20091020 

From marissa: Solve this linear system
2xy=5
3x+y=9 Answered by Penny Nom. 





A right triangle 
20091012 

From Josseph: A right triangle has an area of 84ft sq. and a hypotenuse 25ft long. What are the lengths of the other two sides? Answered by Penny Nom. 





$6.25 in nickels quaters and dimes 
20091010 

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 Answered by Penny Nom. 





Two rectangles 
20091008 

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 Answered by Penny Nom. 





Elimination method 
20091008 

From Kenty: How do I solve this problem using the elimination method?
3x7y=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. Answered by Penny Nom. 





Two equations in two unknowns 
20090918 

From Citizen: x+3y=7
x+4y=7 Answered by Penny Nom. 





Simultaneous equations 
20090828 

From onias: solve 3/a  2/b = 1/2 , 5/a + 3/b = 29/12 Answered by Robert Dawson. 





Two equations in two unknowns 
20090730 

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.
2xy=2 5x+y=5 Thanks for the help Answered by Penny Nom. 





The extended real number system 
20090630 

From Justin: Hi again, thanks a lot for answering my previous question! I was also just wondering again if the extended real number system has a potential or actual infinity because it includes positive infinity as a point that exists at the end of it?
All the Best,
Justin Answered by Robert Dawson. 





Is one Infinity larger than another in the extended real number system? 
20090624 

From Justin: Hello there, I was wondering if one infinity is larger than another in the extended real number system (just like in the transfinite ordinals and cardinals with respect to infinite sets) or are all infinities the same size in the extended real number system? Thanks sooo much for answering my question! I greatly appreciate it!
All the Best,
Justin Answered by Robert Dawson. 





Two equations 
20090531 

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 Answered by Penny Nom. 





Two equations 
20090518 

From Bob: solve the system:
x/2  2y= 8
3x + 2/3y= 10 Answered by Stephen La Rocque. 





The callaway system 
20090426 

From Earl: Do you have a formula to enter players scores using the callaway system that calculate each player score after their score is entered? Answered by Victoria West. 





An infinite number of solutions 
20090324 

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 Answered by Harley Weston. 





A linear system 
20090313 

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 Answered by Harley Weston. 





Linear systems 
20090220 

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. Answered by Penny Nom. 





A rectangular park 
20090206 

From Debbie: A park named Writer's Rectangle opened in town. When asked about the dimensions of the rectangle, the city planner, responded with these clues: The diagonals of the rectangular park plus its longer sides together measure seven times one of the shorter sides. The length of one diagonal is 250 m longer than one of the shorter sides. Use this information to find the area of the park. Answered by Stephen La Rocque. 





The substitution method 
20090206 

From amber: Pleasse help me with this problem
x+y=2
y2x=1 Answered by Penny Nom. 





System of equations  comparison method 
20090102 

From nick: Hi, I am doing a project on system of equations by using comparison method,
but for some reason or another, i can't seem to find any information on the
comparison method at all. So, please would you help me by giving me a website
that you know of that has some information on my method. And, if you know the
answer, can you please tell me why or when do we use system of equations by
using comparison method?
Thank You Answered by Robert Dawson. 





Why is the difference between british and american counting? 
20081215 

From Muhammad: Why is the difference between british and american counting?
Example 1 Billion american = 1,000,000,000 but,
1 Billion British = 1,000,000,000,000 Answered by Robert Dawson and Harley Weston. 





A linear system 
20081022 

From Tiffany: solve:
x + y + z = 4
2x  3y  z = 1
4x + y  2z = 16 Answered by Penny Nom. 





Two equations in two unknowns 
20081017 

From Dushayne: Please help me in solving this problem:
a. 3x4y=32
5x+2y=10
b. 2x+3y=11
4x+3y=10 Answered by Penny Nom. 





Using the augmented matrix 
20081017 

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 Answered by Harley Weston. 





The vertices of a triangle 
20080927 

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=0,4x3y17=0,4x9y+13=0? Answered by Harley Weston. 





A word problem with three numbers 
20080902 

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." Answered by Victoria West. 





Two equations in two unknowns 
20080801 

From James: Question from james, a student:
3x+2y=9;24x2y=18
My math teacher says that it is (2,4)
Can someone please explain how to figure this out by graphing? Answered by Victoria West. 





Simultaneous equations 
20080723 

From Franco: Solve
3 D + E  F = 10
2 D  F = 4
3 D  4 E  F = 25
Franco Answered by Penny Nom. 





solving four simultaneous equations 
20080718 

From Muhammad: 2B2C+4E=1
A+B+C+D=0
2B2C2D+E=0
B+C+4D2E=0 Answered by Janice Cotcher. 





A rectangular room 
20080630 

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? Answered by Penny Nom. 





Cows and chickens 
20080616 

From damebochie: I got this problem and want to write a system of equation for it:
Farmer Joe has cows and chickens on his farm. One day he count 76 legs and 24 heads. How many cows and how many chickens are on the farm? write a system of equations and solve.
I don't have any problem to solve it, but I just can;t see how I am going to write this system of equation.
Thank you so much for helping? Answered by Harley Weston. 





Substitution method 
20080530 

From taquicia: 2yx=3
x=5+y Answered by Janice Cotcher. 





How old are the sisters? 
20080511 

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. Answered by Penny Nom. 





A linear system 
20080310 

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) Answered by Penny Nom. 





Simultaneous equations 
20080229 

From CONOR: I was wondering if you could help me with this problem
7x  5y = 1
3y = 4x Answered by Penny Nom. 





A inear system 
20080203 

From Kelly: is (1,5) a solution of each system? y=x+4 y=1/5x Answered by Penny Nom. 





Two equations in x and y 
20080201 

From leslie: 6x+8y=40 4x+5y=25 Answered by Penny Nom. 





A linear system 
20080122 

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 
20080110 

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 14inch 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 
20080108 

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. Answered by Penny Nom. 





What is the speed of the plane in still air? 
20080105 

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? Answered by Penny Nom. 





System of equations 
20071206 

From Jenn: change the equation,xy=4 to form y=mx+b
the solution to the system of equations y=2x and y=x+3 is Answered by Stephen La Rocque. 





Chicken and goat feet 
20071205 

From Kim: Old McDonald raises goats and chickens. The animals have a total of
100 heads adn 360 feet. How many goats and how many chickens does Mr.
McDonald have? Answered by Stephen La Rocque and Penny Nom. 





An augmented matrix 
20071129 

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 Answered by Harley Weston. 





Four triangles in a square 
20071015 

From Kristina: A square with side lengths of 6 cm is divided into 3 right triangles and a larger isosceles triangle. If the three right triangles have equal area, find the exact area of the isosceles triangle. Answered by Stephen La Rocque. 





Substitution method 
20071011 

From Kevin: 3xx+2y=36y=11 Answered by Stephen La Rocque. 





Solving four simultaneous equations (system of four linear equations) 
20071007 

From Johan: I need some help in solving this question
x + 2y  3z + 4w = 12
2x + 2y  2z + 3w = 10
0 + y + z + 0 = 1
x  y + z  2w = 4 Answered by Stephen La Rocque. 





Two equations in two unknowns 
20070922 

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. 





Two equations in two unknowns 
20070914 

From CAMEILA: NEED T0 SOLVE THIS EQUATION
Y = 2X + 6
Y + 6 = 2x Answered by Stephen La Rocque. 





A nonlinear system 
20070814 

From Marsia: Explain how the solution of a nonlinear system could be just a point, or two points. Sketching these may make it easier Answered by Penny Nom. 





Linear systems and inverses 
20070806 

From Marsia: explain how inverses are used to solve linear systems. Answered by Penny Nom. 





A linear system 
20070629 

From Kim: solve for x,y,z
xy+z=4
2x+2yz=2
x2y+2z=7 Answered by Harley Weston. 





The substitution method 
20070623 

From mary: solve the system by the method of substitution:
5x+2y=15
4xy=9 Answered by Stephen La Rocque. 





A system of linear equations 
20070614 

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? 
20070605 

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. 





System of equations 
20070524 

From Chris: Find all real solutions (x,y,z,w) of the system of equations:
2y= x + x/17, 2z= y + y/17, 2w = z + z/17, 2x= w + w/17 Answered by Penny Nom. 





The substitution method 
20070508 

From A student: I need help on these two problems( substitution method)
2x+7y=10
x3y= 3
and
6x8y= 12 3x+4y=9 Answered by Penny Nom. 





The vertices of a triangle 
20070502 

From natakie: Find the coordinate of the vertices of a triangle whose sides lie on the following three lines.
2x+5y16=0, 4x3y6=0 and 3x+y+2=0 Answered by Penny Nom. 





Two equations 
20070429 

From lavon: I'm having trouble figuring out a linear equation, can you help?
 3x + 2y = 8
3x + 2y = 8 Answered by Penny Nom. 





A linear system 
20070425 

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 Answered by Penny Nom. 





No solution to a linear system 
20070409 

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 
20070323 

From Adam: Solve the system by graphing: 4y>6x
3x+2y<6 Answered by Stephen La Rocque and Penny Nom. 





Simultaneous equations with fractions 
20070228 

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 
20070213 

From Mary: I've been trying for quite some time now to figure this out. I have to solve this by using the GaussJordan Method: 3x  y = 15 2x + 3y = 10 Can anyone help me? Answered by Penny Nom and Gabriel Potter. 





Patrick's new job 
20070202 

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 Answered by Penny Nom. 





The substitution method 
20070131 

From Victoria: how do i solve this problem using the substitution method? 2x5= 14 7x+14y= 5 Answered by Stephen La Rocque. 





The elimination method 
20070131 

From Addrianna: x2y=2 3x5y=7 Answered by Stephen La Rocque. 





An algebra exercise 
20070124 

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 
20070118 

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 
20070104 

From Harold: System A (4, 2/3) 2x3y=6 and x3y=2
I approached this problem using the addition method.
Could i have found the answer using the graphing method? Answered by Penny Nom. 





A system of equations 
20061113 

From Katrina: solve the system of equations using either the substitution or the elimination method. 2x3y= 12 and 4x+6y=15 Answered by Penny Nom. 





Metric conversion 
20061008 

From Eve: 45.6 microliter to megaliter? Answered by Stephen La Rocque. 





Linear systems 
20060921 

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 Answered by Penny. 





Metric Conversions 
20060902 

From Patricia: I have a new difficulty, metric conversion when it involves the prefixes. Some problems I need help with are: Answered by Stephen La Rocque. 





Calculating the belt length of a three pulley system 
20060716 

From Mark: I have a 3 pulley system with sides abc and pulleys ABC. Pulley A has radius of 10cm, pulley B has radius of 20cm, and pulley C has radius of 3cm. The side lengths are: (center to center of pulleys) between pulleys AB = 75cm, between pulleys BC = 100cm, and between pulleys AC = 50cm. I set these side lengths up as (according to law of sines and cosines) a = 100cm, b = 50cm, and c = 75cm. What is the length of the belt required for this system? I need to know how I would set this problem up and solve. Answered by Stephen La Rocque. 





Three people go to a store where there is a sale 
20060530 

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. Answered by Stephen La Rocque. 





2x+5y=3 And x+3y=7 
20060403 

From Lloyd: simplify 2x+5y=3 And x+3y=7
Answered by Penny Nom. 





2x+3y=0 and 3xy=0 
20060314 

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 3xy=0 this is one question can you help me please Answered by Penny Nom. 





One boundary of a pond is parabolic in shape. 
20060120 

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. Answered by Penny Nom. 





Simultaneous Equations 
20051221 

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? Answered by Penny Nom. 





Solving a pair of equations 
20051110 

From Steven: what is answer to
2 x + y = 1
y = ^{1}/_{3} x  4 Answered by Penny Nom. 





A system of equations 
20050902 

From Gina: How do you interpret the solution of a system of equations by the corresponding graph? Demonstrate your answer by the use of an example. Answered by Penny Nom. 





The substitution method 
20050628 

From Addie: how do i know where to began the substitution method? how do i solve
y = x + 1
2x  y = 1 Answered by Penny Nom. 





y = x+2 and y = 2x  1 
20050503 

From Kimberley: Question:
y=x+2
y=2x1 Answered by Penny Nom. 





Perfecting an ideal gambling system 
20050306 

From Gaz: I am a screenwriter, currently in the fortunate position of having the development of a Screenplay funded by the South Australian Film Corporation. The (anti)hero of this screenplay is a statistician whose life is falling apart around him, thanks in part to his obsession with perfecting an "ideal" gambling system. Answered by Andrei Volodin. 





The substitution method 
20041128 

From A student: I Was working and i ran into this problem can you help me solve it using the substitution method?
3x2y=10
x+5y=27 Answered by Penny Nom. 





Solve for a and t 
20041023 

From Justin: How do I solve for "a" and "t" in the equations:
1000t= 4000 + 2000t + (1/2)at^2
1000=2000 + at Answered by Penny Nom. 





The substitution method 
20040214 

From Keisha: I need to solve this problem by using the substitution method.
3x+y=1
x=2y+5
Please help me understand the method to solve. Answered by Penny Nom. 





Mr.Carter is very cautious 
20031126 

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? Answered by Harley Weston. 





Systems of equations 
20031119 

From Scott: I hope that u can help me....I
am a college student taking a class in Pre Calculus.....I have homework
due this Friday and it counts a BIG Percentage on my FINAL grade.....I
am getting mixed up and can not figure out a few problems.....Please help
me.....
Method Of Subsitution
Problem 1. y 8x = 5
x(squared) + y(squared) = 25
Problem 2. y = x(squared)  2x  6
Y = x(squared)  4
Answered by Penny Nom. 





Substitution method 
20030914 

From John:
Hello, my name is john and while I was finishing up my work I stumbled into these problems. a/4b=1 a+b=11 and 6ab=5 4a3b=8 Thanks a lot. I really need some help :) John Answered by Penny Nom. 





The metric and Imperial systems 
20030608 

From Ashlee: i am a year 8 student, and i am doing my Maths talent quest on the Metric and Imperial number system.
i was wondering, where did the 2 systems orginate and if possible, a little bit or information.
I also need to know the conversions of ounce, foot, mile..etc..from imperial to metric. Answered by Penny Nom. 





______cm=0.048km 
20030227 

From Antonette: ______cm=0.048km Answered by Penny Nom. 





Millilitres and millimeters 
20030209 

From Iwan: I was just wondering whether a millilitre was equal to a millimetre, if not, what is there difference. Answered by Penny Nom. 





Two equations in two unknowns 
20030206 

From Patrick: What are all ordered pairs of real numbers (x, y) for which: y^{x2  7x + 12} = 1 and x + y = 6? Answered by Penny Nom. 





Milliliters 
20030204 

From James: What is a milliliter? Answered by Penny Nom. 





The intersection of conics 
20021219 

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. 





How many billions equal one trillion? 
20021207 

From Ryan and Aylah: How many billions equal one trillion? We believe that the answer is one thousand times one billion equals one trillion. Please help us with the answer to this question. Answered by Penny Nom. 





x + y=80 and x + z=100 
20021128 

From PJ: x + y=80 x + z=100 can you solve for x, y or z? Answered by Penny Nom. 





The substitution method 
20021115 

From A student: Solve by using the substitution method. x = 3y  1 x + 2y = 9 Answered by Penny Nom. 





Determining a parabola 
20021106 

From Shelley: let (0,3) and (1,9)and (1,1) be given points in a parablola. Determine a b and c Answered by Penny Nom. 





A million sheets of 30 cm long paper 
20020915 

From Jennifer: if you put a million sheets of 30 cm long paper end to end, how many kilometer long would the paper be from begining to end? Answered by Penny Nom. 





Two equations 
20020726 

From Derek: 1. 3x + 2y = 4 2. 7x + 2y = 24 finding x and y. Answered by Penny Nom. 





Some inequalities 
20020725 

From A student:
1)5 <= 3X+1 < 1 2)4X2 < 6 OR X+2 > 9 Answered by Penny Nom. 





An augmented matrix 
20020420 

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 ab9c=5 Answered by Penny Nom. 





Pairs of equations 
20020404 

From A student:
high school level student is asking
y=4x x=4y
x+y=5 3x+2y=20
y=x1 3xy=4
x+y=3 2x3y=9
x+5y=4
3x+15y=1
. . .
Answered by Penny Nom. 





The substitution method 
20020224 

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 Answered by Penny Nom. 





Simultaneous equations 
20011217 

From Matthew: 4x + y = 4 2x  3y = 5 what is x and y Answered by Penny Nom. 





Two equations in two unknowns 
20011204 

From Courtney: y = 3x + 2 y = 4x  5
solve for x Answered by Penny Nom. 





Matrix 
20011121 

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. 





Counting CD's 
20011106 

From Jason: An older brother said to his younger brother, "Give me 8 of your CDs, then I will have twice as many as you." The younger brother replied, "No, you give me 8 of yours instead, and then we'll have an equal number." How many CDs does each boy have? Answered by Chris Fisher. 





Common solution 
20010602 

From Samantha:
 Solve for common solution: x+y=6 2x3y=2
 Solve for y in terms of x: 3xy=4
Answered by Penny Nom. 





Matrices 
20010326 

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 
20010316 

From joy: How do u solve problems using systems of equations? ~ finding x and y~ ex:
26 = 3x  2y 42 = 4x + y Answered by Penny Nom. 





The substitution method 
20010305 

From A student: Solve each system of equations by the substitution method. Show your work.  y = 8
7x = 1  y
 y = x  1
4x  y = 19 Answered by Penny Nom. 





Solving Equations 
20010223 

From Stephanie: Do you know who came up with solving equations? Do you have any websites 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? Answered by Juci McDonald. 





Two linear equations 
20000914 

From David Dean: 2a + 1b = 3.39 3a + 3b = 6.59 What formula do I use to find what a = ? Answered by Harley Weston. 





Two linear systems 
20000801 

From A student: please help me with this homework question. 5/x + 6/y= 19/6 3/x + 4/y =2 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. Answered by Penny Nom. 





A bar over a Roman numeral 
20000621 

From Charles Fontaine: Is there any significance to the bar placed over some Roman numerals? Answered by Penny Nom. 





The equation of a parabola 
20000522 

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 = ax^{2} + bx + c. Answered by Penny Nom. 





A matrix equation 
20000514 

From A student: Right now, we are dealing with matrices and we are supposed to solve the following problem on our graphingcalculators: 2a+3b4c+d=20 a2b+3c5d=14 3a+4b2c+3d=19 5ab+6c+4d=5 Answered by Penny Nom. 





History of a meter 
20000407 

From Jarod Fischer: The length of a meter has been determined in three different ways. The first and original way was determined in 1798. The second way was determined in 1960. The third and current way was determined in 1983. What were the three ways and why were the first two abandoned? Answered by Harley Weston. 





Taxis in Chicago 
20000327 

From A high school studenthigh 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? Answered by Harley Weston. 





A system of equations in five unknowns 
20000320 

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 . . . Answered by Penny Nom. 





Simultaneous equations 
20000311 

From Laura Molck: My name is Laura Molck and I am in Year 11 in Australia. Please help me with the following. I know that they are all simultaneous equations which I can do but I have trouble with the formulae to work the equations. Can you please help!! 1. A tent manufacturer produces 2 models, Outback and Bushwalker. From earlier sales records it is known that 20% more of the Outback model is sold than the Bushwalker. A profit of $200 is made on each Outback sold, but $350 is made on each Bushwalker. If during the next year a profit of $177,000 is planned how many of each model must be sold? Answered by Penny Nom. 





Systems of linear equations 
20000310 

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 Answered by Penny Nom. 





Systems of equations 
19991206 

From Roger Hornbaker: I am having problem figuring out x and y solutions.  5x + y = 4
3x  y = 4  3x + 2y = 6
 3x + y = 0 Answered by Penny Nom. 





Metric Conversion 
19990307 

From TDestra: Please help to answer this question: Is a cubic centimeter equivalent to milligrams or milliliters, and how many? Also, is it a liquid measure? Answered by Penny Nom. 





Linear systems of equations 
19981116 

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=b1, 3a+ b=3 b) verify your solutin in a I dont understand it. please help Answered by Jack LeSage. 





A Linear System 
19981008 

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 Answered by Penny Nom. 





Number Systems 
19981007 

From Frans: What other number system are there besides the real number system and the complex number system? Interested adult thanks Answered by Penny Nom. 





Graph question 
19980512 

From Rose Seminary: Why is the point of intersection of two lines the solution to the corresponding system of equations? Answered by Penny Nom. 





Combien d'éleves fréquentent cette école? 
20080404 

From Jeff: Une ecole compte sept fois plus d'éleve que d'enseignants et enseignantes .De plus , le nombre de membres du personnel non enseignant correspond a la moitié du nombre d'enseignats et enseignantes . Si l'on tient compte de l'ensemble des éleves , du personnel enseignant et du personnel non enseignante , on dénombre 714 personnes . Combien d'éleves fréquentent cette école? Answered by Antoine Letarte. 





Système à deux équations 
20071211 

From Fabrice: un rectangle a 130 m pour périmetre. si on diminue sa longueur de 1 m et on augmente sa largeur de 1 m, l'aire augmentera de 14m².
trouver les deux dimentions du rectangle. (on trouvera, au préalable, la difference des deux dimensions) Answered by Claude Tardif. 

