Question

Use the elimination method to solve the linear-quadratic system y=x2−2x−2
, y=2x−6
.(1 point)
Responses

(2,−2)
and (−2,2)
left parenthesis 2 comma negative 2 right parenthesis and left parenthesis negative 2 comma 2 right parenthesis

(−2,−2)
and (−2,2)
left parenthesis negative 2 comma negative 2 right parenthesis and left parenthesis negative 2 comma 2 right parenthesis

(2,−2)
left parenthesis 2 comma negative 2 right parenthesis

(−2,−10)

Answer 1

Set the two expressions for y equal:
x^2 − 2x − 2 = 2x − 6.
Bring all terms to one side:
x^2 − 4x + 4 = 0 → (x − 2)^2 = 0, so x = 2.
Then y = 2x − 6 = 4 − 6 = −2.

Solution: (2, −2).