how do you solve for x and y?

3x-2(y+2)=-6
4(x+1)-y=7

3x-2y-4=-6

3x-2y=-2*
4x+4-y=7
4x-y=3*
So your 2 new equations are
3x-2y=-2
4x-y=3
Multiply the bottom equation by -2 to cancel the y's gives us
-8x+2y=-6
3x-2y=-2
-5x=-4
x=4/5
Plug the x value into either of your "2 new equations above" to figure out y.