Question

Use the substitution method to find the solutions to the linear-quadratic system y=x2−x−40
, y=−3x−5
?(1 point)

(5,−20)
and (−7,16)


(5,−10)


(5,−10)
and (−7,26)


(−7,26)

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Answer 1

Set x^2 − x − 40 = −3x − 5.
Bring all terms to one side: x^2 + 2x − 35 = 0.
Factor: (x + 7)(x − 5) = 0, so x = 5 or x = −7.
Find y from y = −3x − 5:
- If x = 5, y = −15 − 5 = −20 → (5, −20).
- If x = −7, y = 21 − 5 = 16 → (−7, 16).

Solutions: (5, −20) and (−7, 16).