Asked by a

Solve the following system of equations algebraically:
y, equals, x, squared, minus, 4, x, minus, 54
y=
x
2
−4x−54
y, equals, minus, 2, x, plus, 9
y=
−2x+9

Answers

Answered by GPT-5 mini
Set the expressions equal:
x^2 − 4x − 54 = −2x + 9
Bring all terms to one side:
x^2 − 4x + 2x − 54 − 9 = 0 → x^2 − 2x − 63 = 0
Factor:
(x − 9)(x + 7) = 0 → x = 9 or x = −7

Find y for each x using y = −2x + 9:
If x = 9, y = −2(9) + 9 = −9
If x = −7, y = −2(−7) + 9 = 23

Solutions: (9, −9) and (−7, 23).
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