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)