Since x + y = -3 ---> x = -3 - y
Substituting into y = -x2 - 5x - 6
---> y = -(-3 - y)2 - 5(-3 - y) - 6
y = -(9 + 6y + y2) + 15 + 5y - 6
y = -9 - 6y - y2 + 15 + 5y - 6
y2 + 2y = 0
y(y + 2) = 0
So: either y = 0 or y = -2
Now, find out the corresponding values for x to get your two ordered pairs.