Question

Use elimination to solve each system of equations
2x-y=-1
3x-2y=1

Answer 1

2x - y = -1
3x - 2y = 1
5x - 3y = 0
5x - 5x - 3y = 0 - 5x
3y = 0 - 5x
3y = 0 - 5x
3 3
y = 0 - 5/3x
3x - 2(0 - 5/3x) = 1
3x + 8/3x = 1
5 1/4x = 1
5 1/4x = 1
5 1/4 5 1/4
x = 4/21
3(4/21) - 2y = 1
4/7 - 2y = 1
-4/7 -4/7
-2y = 3/7
-2y = 3/7
-2 -2
y = -3/14
(x, y) = (4/21, -3/14)

Answer 2

`2x-y=-1 \ \ \ |* (-2) \\ 3x-2y=1 \\ \\ -4x+2y=2 \\ \underline{3x-2y=1 \ \ \ \ } \\ -4x+3x=2+1 \\ -x=3 \ \ \ |* (-1) \\ x=-3 \\ \\ 2x-y=-1 \\ 2 * (-3)-y=-1 \\ -6-y=-1 \ \ \ |+6 \\ -y=5 \ \ \ |* (-1) \\ y=-5 \\ \\ \boxed{(x,y)=(-3,-5)}`