Question

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)

Answer 1

​(−1, 0)​ and (0, 6)

Explanation:

Answer 2

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)