-4x +7y = 9
5x +2y = -22
Multiply the top equation by 5 and the bottom equation by 4
-20x +35y = 45
20x +8y = -88
Now add the equations:
-20x +35y = 45
20x +8y = -88
0x +43y = -43
simplify
43y = -43
y = -43/43
y = -1
pick one of the original equations
5x + 2y = -22
enter the value for y
5x +2(-1) = -22
5x -2 = -22
solve for x
5x = -20
x = -4
Answer: x = -4, y = -1
Check:
-4x +7y = 9
-4(-4) + 7(-1) = 9
16 - 7 = 9 True
Check:
5x + 2y = -22
5(-4) + 2(-1) = -22
-20 -2 = -22 True