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

Let's start by using the elimination method. We can add the two equations together to eliminate the variable x:

-2x - 5y = -12

-2x + 5y -5y - 2x = -24
-4x = -24
x = 6

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

-2(6) - 5y = -12
-12 - 5y = -12
-5y = 0
y = 0

Therefore, the solution to the system of equations is x = 6 and y = 0.