Question

find the solutions to the system of nonlinear equations given by:
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$$\begin{cases} y = -2x + 5 \\\\ y = -x^2 + 5 \\end{cases}$$

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use the graph to determine which point is a and b.
enter your answer as an ordered pair. for example: \\((2, -5)\\)

Explanation:

Step1: Equate the equations

$$-2x + 5 = -x^2 + 5$$

Step2: Solve for x

$$x^2 - 2x = 0 \implies x(x - 2) = 0 \implies x = 0 \text{ or } x = 2$$

Step3: Find corresponding y-values

$$x = 0 \implies y = 5$$

$$x = 2 \implies y = 1$$

Step4: Match with graph points

$$A = (2, 1), B = (0, 5)$$

Answer:

A: \((2, 1)\)
B: \((0, 5)\)