What are the solutions to the system of equations?

y = -x^2 -5x -6      (1)

x + y = -3     →    y = -3 -x     (2)

Sub (2)  into (1)  for   y    and we have

-3 - x = -x^2  - 5x   - 6        add  3 , x to  both sides

-x^2 - 4x  - 3   = 0             multiply through  by  -1

x^2 + 4x + 3  =  0    factor

(x + 3)  ( x + 1)  = 0

Set both fctors to 0  and solve for x and we get that

x = -3   and     x = -1

And when x = -3   y  =  0

And when  x =  -1     y = -2

So you are CORRECT  !!!    [ good job  !!! ]