So you can solve for either variable in equation 2.
I'll solve for x.
x = -1 - y

So we can plug this into Equation 1.
(-1 - y) * y = -240
-y - y^2 = -240

By moving everything to one side you will get:
y^2 + y - 240 = 0

By solving this through the quadratic formula you will get:
y = 15, -16

Now plug this into your either of your original equations:
x + y = -1

If y = 15
x + 15 = -1
so x = -16

if y = -16
x - 16 = -1
so x = 15

In either situation you will get 15 or -16. So the answer is 15 and -16.

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