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)

Answer:

The solutions of the system are:

(-1, 0) and (0, - 6)