x-4x+12=6
-3x+12=6
-3x+12-12=6-12
-3x=-6
-3x/-3=-6/-3
x=2
Plug (2) in for x in L2 and solve for y:
y=2(2)-6
y=4-6
y=-2
The solution (x,y)=(2,-2)
Check in both equations by substituting (x,y)=(2,-2) and see if it equals out:
L1) (2)-2(-2)=6
2+4=6
6=6 L1 checks out.
L2) (-2)=2(2)-6
-2=4-6
-2=-2 L2 checks out also, so we can say with confidence that the solution is right.