Solve the system of equations.
y= x2 - 6
y=-2x + 9

(3,3)

(-5,19)

Step-by-step 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)

the first one, all those points on the line just make a strait line.