2x - 5y = 24
x + y = -2
multiply the bottom equations by 5
2x - 5y = 24
5x + 5y = -10
add the bottom equation to the top equations
7x + 0y = 14
5x + 5y = -10
divide the top equation by 7 on both sides
x + 0y = 2
5x + 5y = -10
the top equations tells us x = 2
multiply the top equation by -5 on both sides
-5x + 0y = -10
5x + 5y = -10
add the top equation to the bottom equation
-5x + 0y = -10
0x + 5y = -20
divide the bottom equation by 5 on both sides
-5x + 0y = -10
0x + y = -4
the bottom equation tells us y = -4
Answer: x = 2, y = -4