Question

Use the elimination method to solve the linear-quadratic system y=x2+x−42
, y=−x+6
.(1 point)
Responses

(−8,14)
and (6,0)
open paren negative 8 comma 14 close paren and open paren 6 comma 0 close paren - no response given

(8,−2)
and (−6,12)

Answer 1

Set the two expressions for y equal:
x^2 + x − 42 = −x + 6
Bring all terms to one side:
x^2 + 2x − 48 = 0
Factor:
(x + 8)(x − 6) = 0
So x = −8 or x = 6. Then y = −x + 6 gives y = 14 when x = −8, and y = 0 when x = 6.

Solutions: (−8, 14) and (6, 0).