To solve this system of equations, let's first simplify the first equation:
-6x + 4y = -12

Now we have the system of equations:
-6x + 4y = -12
6x - 5y = 3

Adding the two equations together, we get:
-y = -9
y = 9

Now substitute y = 9 into one of the equations, for example the second equation:
6x - 5(9) = 3
6x - 45 = 3
6x = 48
x = 8

Therefore, the solution to the system of equations is x = 8, y = 9.