Answer:
(3,3)
(-5,19)
Explanation:
y= x^2 - 6
y=-2x + 9
Set the two equations equal to each other y=y
x^2 - 6 =-2x + 9
Add 2x to each side
x^2 +2x- 6 =-2x+2x + 9
x^2 +2x- 6 = 9
Subtract 9 from each side
x^2 +2x- 6-9 =9- 9
x^2 +2x- 15 =0
Factor the left hand side
What 2 numbers multiply to -15 and add to 2
-3 *5 = -15
-3+5 = 2
(x-3) (x+5) =0
Using the zero product property
x-3 =0 x+5 =0
x=3 x=-5
Now we find y for each x
x=3
y=-2(3) + 9 = -6+9 =3
(3,3)
x=-5
y=-2(-5) + 9 = 10+9 =19
(-5,19)