What are the solutions of the system?

{y=−6x−6y=x2−5x−6

(0, −1) and (−6, 0)

(−1, 0) and (−6, 0)

(−1, 0) and (0, −6)

(0, −1) and (0, −6)

We have the following system of equations:
 y = -6x-6
 y = x2-5x-6
 Matching we have:
 x2-5x-6 = -6x-6
 Rewriting we have:
 x2-5x-6 + 6x + 6 = 0
 x2 + x = 0
 Rewriting:
 x (x + 1) = 0
 The solutions are:
 x = 0
 x = -1
 For x = 0
 y = -6 (0) -6 = 0-6 = -6
 y = -6
 For x = -1
 y = -6 (-1) -6 = 6-6 = 0
 y = 0
 The solutions are:
 (x, y) = (0, -6)
 (x, y) = (- 1, 0)
 
 The solutions of the system are:
 (-1, 0) and (0, -6)