Question

assignment 11.5: solve systems of nonlinear equations
score: 13/17 answered: 6/8
question 7
find all solutions of the system:
\

$$\begin{cases} y = 64 - x^2 \\\\ y = x^2 - 64 \\end{cases}$$

the two solutions of the system are:
enter your answer as a list of ordered pair. for example: (2, -5), (5, -2)
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Explanation:

Step1: Set the two equations equal

Since \(y = 64 - x^{2}\) and \(y=x^{2}-64\), we set \(64 - x^{2}=x^{2}-64\).

Step2: Solve for \(x\)

Add \(x^{2}\) to both sides: \(64=2x^{2}-64\).
Add \(64\) to both sides: \(128 = 2x^{2}\).
Divide both sides by \(2\): \(x^{2}=64\).
Take square roots: \(x=\pm8\).

Step3: Solve for \(y\)

When \(x = 8\), substitute into \(y=x^{2}-64\), \(y=8^{2}-64=64 - 64=0\).
When \(x=-8\), substitute into \(y=x^{2}-64\), \(y=(-8)^{2}-64=64 - 64=0\).

Answer:

\((8,0),(-8,0)\)