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

From the second equation, we can write y = -3 - x and substitute it into the first equation:

x^2 - (-3 - x)^2 = -21
x^2 - (9 + 6x + x^2) = -21
x^2 - 9 - 6x - x^2 = -21
-6x - 9 = -21
-6x = -12
x = 2

Now that we have found the value of x, we can substitute it back into the second equation to find y:

2 + y = -3
y = -5

Therefore, the solution to the system of equations is x = 2 and y = -5.