Question

What are the solutions of the system?

Answer 1

-6x-6=x²-5x-6
x²+x=0
x(x+1)=0
x=0, x=-1
x=0, y=-6x-6=-6*0-6=-6      (0,-6)
x=-1, y=-6x-6=-6*(-1)-6=0    (-1,0)

Answer (-1.0) and (0,-6) . The last one.

Check
(0,-6), y=-6-x,   -6=-6-0, -6=-6  True
y=x²-5x-6, -6=0+0-6,  -6=-6,  True
(-1,0),y=-6-x,   0=-6-(-6), 0=0  True
y=x²-5x-6,    0=1²-5(-1)-6=1+5-6=6-6=0,    0=0 True,

So,
Answer (-1.0) and (0,-6) . The last one.