Question

2
a system of equations is given.
$y = x^2 - 9$
$y = -2x - 1$
what is one solution to the system of equations?
( , )

Explanation:

Step1: Set the equations equal

Since both equal \( y \), set \( x^2 - 9 = -2x - 1 \).

Step2: Rearrange into quadratic form

Bring all terms to one side: \( x^2 + 2x - 8 = 0 \).

Step3: Factor the quadratic

Factor: \( (x + 4)(x - 2) = 0 \).

Step4: Solve for \( x \)

Set each factor to zero: \( x + 4 = 0 \) or \( x - 2 = 0 \), so \( x = -4 \) or \( x = 2 \).

Step5: Find corresponding \( y \)

For \( x = -4 \): \( y = -2(-4) - 1 = 7 \).
For \( x = 2 \): \( y = -2(2) - 1 = -5 \).

Answer:

\((-4, 7)\) (or \((2, -5)\))