Question

Question was provided via image upload.

Explanation:

Step1: Substitute y from first equation into second

From \( y = -x^2 - 11x \), substitute into \( x + y = 9 \):
\( x + (-x^2 - 11x) = 9 \)

Step2: Simplify the equation

Simplify: \( -x^2 - 10x - 9 = 0 \)
Multiply by -1: \( x^2 + 10x + 9 = 0 \)

Step3: Factor the quadratic

Factor: \( (x + 1)(x + 9) = 0 \)

Step4: Solve for x

Set each factor to 0:
\( x + 1 = 0 \Rightarrow x = -1 \)
\( x + 9 = 0 \Rightarrow x = -9 \)

Step5: Find corresponding y values

For \( x = -1 \):
\( y = 9 - x = 9 - (-1) = 10 \)

For \( x = -9 \):
\( y = 9 - x = 9 - (-9) = 18 \)

Answer:

\((-1, 10)\) and \((-9, 18)\)