Solve using substitution.

y = x + 2

y − x = 8

sec. 8.2 #30

solve using the elimination method.

5x − 3y = 8

-5x + y = 4

i tried solving but the x's in the first problem cancelled each other out and now i'm confused

You're right-when you try to do a substitution you get nonsense. Think about it-if you rewrite y - x = 8 to be y = x + 8, and the other equation is y = x + 2, there are NO SOLUTIONS that would satisfy (x,y) for BOTH equations.
The second problem you can just add so that you eliminate 5x, and you get -2y = 12; y = -6; replace back into the equation:
-5x + -6= 4
-5x = 10
X = -2, then check your work