Equations given:
10x+4y=12
x-4y=10
Step 1: Cancel out the y to find x (because one is positive 4y and one is negative 4y, they cancel each other out)
10x+4y=12
x-4y=10
11x=22
x=2
Step 2: Plug x back into one of the equations (I chose the second one b/c it was easier but it doesn't matter. You should get the same answer either way)
x-4y=10
2-4y=10
-4y=8
y=-2
Optional step: if you plug the answers back into the equations, you should get the right answers.