6x - y = -8
y = 6x + 8 - not plug this in the first equation
4x - y = -3
4x - (6x + 8) = -3
4x - 6x - 8 = -3
-2x = -3+8
-2x = 5
x = 5/(-2)
x = -5/2
Now we can solve for y.
As we said before, y = 6x + 8
y = 6* (-5/2) + 8
y = -15 + 8
y = -7
{x,y} = {-5/2,-7} is the solution to the system