Question

question 11 (multiple choice worth 5 points) (02.02h mc) the elimination method was used to solve the following system of equations: $x^2 - y = -4$ $x^2 + y^2 = 16$ which of the following is the correct y-coordinate of the solution? 4 0 -3 -5

Explanation:

Step1: Isolate $x^2$ from first equation

From $x^2 - y = -4$, we get:
$x^2 = y - 4$

Step2: Substitute $x^2$ into second equation

Replace $x^2$ in $x^2 + y^2 = 16$:
$(y - 4) + y^2 = 16$

Step3: Simplify to quadratic equation

Rearrange and combine terms:
$y^2 + y - 4 - 16 = 0$
$y^2 + y - 20 = 0$

Step4: Factor the quadratic equation

Find factors of -20 that sum to 1:
$(y + 5)(y - 4) = 0$

Step5: Solve for y

Set each factor equal to 0:
$y + 5 = 0 \implies y = -5$; $y - 4 = 0 \implies y = 4$
Verify solutions: For $y=-5$, $x^2 = -5 -4 = -9$ (invalid, no real solution). For $y=4$, $x^2 = 4-4=0$ (valid, $x=0$).

Answer:

4