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

First, isolate x in the second equation:
x = y + 4

Now we can substitute this expression for x in the first equation:
2(y + 4) + 3y = -7
2y + 8 + 3y = -7
5y + 8 = -7
5y = -15
y = -3

Now that we have found the value of y, we can substitute it back into the equation x = y + 4 to find x:
x = -3 + 4
x = 1

Therefore, the solution to the system of equations is x = 1 and y = -3.