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

Let's use the method of substitution.

From the first equation, we can solve for x in terms of y:
2x + 3y = -2
2x = -3y - 2
x = (-3y - 2)/2
x = -3/2y - 1

Now, substitute this expression for x into the second equation:
3(-3/2y - 1) - 2y = -3
-9/2y - 3 - 2y = -3
-9/2y - 2y = 0
-13/2y = 0
y = 0

Now that we have found the value of y, we can substitute it back into the first equation to find the value of x:
2x + 3(0) = -2
2x = -2
x = -1

Therefore, the solution to the system of equations is x = -1 and y = 0.