Question

Use the elimination method to solve
the linear-quadratic system
, .
(1 point)
y = x + x − 42
2 y = −x + 6
(−8, 14) and (6, 0)
(6, 0)
(−8, 14)
(8, −2) and (−6, 12)

Answer 1

Set the two expressions for y equal to eliminate y:
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. Find y using y = −x + 6:
For x = −8: y = 8 + 6 = 14 → (−8, 14)
For x = 6: y = −6 + 6 = 0 → (6, 0)

Solutions: (−8, 14) and (6, 0).