Question

Which of the following uses the substitution method to solve linear-quadratic system y=x2+3x+6
, y=−6x−12
?(1 point)
Responses

(−6,24)
and (−3,6)
left parenthesis negative 6 comma 24 right parenthesis and left parenthesis negative 3 comma 6 right parenthesis

(−3,6)
left parenthesis negative 3 comma 6 right parenthesis

(−6,24)
left parenthesis negative 6 comma 24 right parenthesis

(6,−48)
and (3,−30)

Answer 1

Set x^2+3x+6 = -6x - 12. Then
x^2 + 9x + 18 = 0 → (x+3)(x+6)=0, so x = -3 or x = -6.
For x = -3, y = -6(-3)-12 = 6. For x = -6, y = -6(-6)-12 = 24.

Solution: (−6, 24) and (−3, 6).