Solve the following system by the elimination method. check the solution. 5x−5 = −7y, 3x+2y = - 8

5x-5=-7y
3x+2y=-8

First, you need to rearrange the first equation so it is in the same format as the second one.
5x-5=-7y
Add 5 to both sides
5x-5+5=-7y+5
Add 7y to both sides
5x+7y=-7y+7y+5
So you have 5x+7y=5

Now you need to multiply that equation by 3
3(5x+7y=5)
15x+21y=15

Multiply the second equation by -5
-5(3x+2y=-8)
-15x-10y=40

Now add them together
15x+21y=15
+(-15x-10y=40)

11y=55
y=5

Now plug y=5 into one of the original equations and solve for x.
3x+2(5)=-8 
3x+10=-8
3x=-8-10
3x=-18
x=-6

To check the solution plug them both into the other equation:
5(-6)-5=-7(5)
-30-5=-35
-35=-35

It checks.

Hope that helps.