NOTE: This system represents a parabola intersecting a circle. We expect:

If we subtract the first line from the second, we have:

y2y = 25 − 5

y2y − 20 = 0

(y + 4)(y − 5) = 0

So y = −4 or 5

The corresponding x values are going to be:

`x = +3` or ` −3`, and `x = 0`

So the solution set will be:

`(−3,−4)`, `(3,−4)` and `(0,5)`.

The sketch shows:

123456-1-2-3-4-5-6123456-1-2-3-4-5-6xyOpen image in a new page

Graphs of `y = -x^2+5` and `x^2+y^2=25`: Intersection parabola and circle

We can see from the graph that our 3 solutions `(−3,−4)`, `(3,−4)` and `(0, 5)` are correct.

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