Answer
(5,0)
Work Step by Step
Our two equations are:
1. 2x=5(2-y)
2. y=3(-x+5)
First lets simplify by distributing the 5 in the first equation and the 3 in the second equation. Our two equations look this:
1. 2x=10-5y
2. y=-3x+15
For the first equation lets bring all of the x and y terms on one side of the equation.
2x=10-5y (add 5y on both sides)
2x+5y=10
Now do the same for the second equation.
y=-3x+15 (add 3x to both sides)
3x+y=15
Now our two equations look like this:
1. 2x+5y=10
2. 3x+y=15
Now lets multiply the bottom (aka. the second) equation by 5.
1. 2x+5y=10
5(3x+y=15)
2. 15x+5y=75
Now subtract the second equation from the first equation in order to eliminate the y terms
-13x=-65
Solve for x by dividing both sides by -13. You get:
x=5
Now that we know the value of x, substitute into our simplified first equation to find the value of y.
2(5)+5y=10
10+5y=10 (subtract 10 from both sides)
5y=0 (divide both sides by 5)
y=0
So our ordered pair is (5, 0)
