To solve this system of equations, we can use the elimination method.

First, let's multiply the first equation by 2 and the second equation by 3 to make the coefficients of y the same:

10x - 4y = -24
9x + 12y = -6

Now let's add these two equations together:

10x - 4y + 9x + 12y = -24 + (-6)
19x + 8y = -30

Now let's solve for x:

19x + 8y = -30
19x = -30 - 8y
x = (-30 - 8y) / 19

Now we can substitute this expression for x into one of the original equations, let's use the first equation:

5x - 2y = -12
5((-30 - 8y) / 19) - 2y = -12
(-150 - 40y) / 19 - 2y = -12
-150 - 40y - 38y = -12 * 19
-150 - 78y = -228
78y = -78
y = -1

Now that we have found the value of y, we can substitute it back into one of the original equations to solve for x. Let's use the first equation:

5x - 2y = -12
5x - 2(-1) = -12
5x + 2 = -12
5x = -14
x = -14 / 5
x = -2.8

So the solution to the system of equations is x = -2.8 and y = -1.