The solution to the system of equations is x = 4 and y = 2.
Let's solve the system of equations:
4x - 12y = -8
-3x + 12y = 12
We can solve this system using the method of addition or elimination. Adding the two equations eliminates y:
(4x - 12y) + (-3x + 12y) = -8 + 12
Simplifying:
4x - 3x = 4
x = 4
Now that we have found x = 4, we can substitute this value back into one of the original equations to solve for y. Let's use the second equation:
-3x + 12y = 12
-3(4) + 12y = 12
-12 + 12y = 12
12y = 12 + 12
12y = 24
y = 24 / 12
y = 2