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Question 1098182: How do I make a word problem that has an answer of (10,20) using Systems of Linear Equation in Two Variables?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! you want y to be equal to 20 when x is equal to 10.
let x represent the number of boys in a class and let y represent the number of girls in a class.
let the total number of students in the class equal 30.
your first equation is x + y = 30
if the ratio of boys to girls is 1/2, then your second equation would be:
x/y = 1/2
if you solve for y, you get y = 2x.
if you convert that into the standard form of a linear equation, you get -2x + y = 0
your two linear equations are:
x + y = 30
-2x + y = 0
you would solve this like any linear equation.
multiply sides of the first equation by 2 and leave the second equation as is to get:
2x + 2y = 60
-2x + y = 0
add the equations together to get 3y = 60
solve for y to get y = 20
replace y with 20 in either of the original two equations to solve for x.
i used the first original equation of x + y = 30
when y = 20, you solve for x and get x = 10.
your solution is x = 10 and y = 20 which can be shown as (x,y) = (10,20)
to confirm the solution is correct, replace x and y with 10 and 20 in both original equations to see if those equations hold true.
first equation of x + y = 30 becomes 10 + 20 = 30 which is true.
second equation of -2x + y = 0 becomes -20 + 20 = 0 which is also true.
the solution of x = 10 and y = 20 is confirmed to be good.
note:
you would also have converted y = 2x into 2x - y = 0 and the answer would have been the same.
-2x + y = 0 becomes 2x - y = 0 when you multiply both sides of that equation by -1.
your two equations would have been:
x + y = 30
2x - y = 0
add those equations together and you get 3x = 30.
solve for x to get x = 10.
solve for y to get y = 20.
same answer.
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