SOLUTION: Solve nonlinear system by substitution. x^2+y^2=25 x^2-y=5

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Question 250436: Solve nonlinear system by substitution.
x^2+y^2=25
x^2-y=5
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!

1.x%5E2%2By%5E2=25
2.x%5E2-y=5
This solves the intersection of a parabola and a circle.
From 2,
x%5E2=y%2B5
Subsitute into 1.
x%5E2%2By%5E2=25
%28y%2B5%29%2By%5E2=25
y%5E2%2By-20=0
%28y%2B5%29%28y-4%29=0
Two solutions:
y+5=0
y=-5
Then
x%5E2=y%2B5
x%5E2=5%2B5=0
x=0
.
.
.
y-4=0
y=4
Then
x%5E2=y%2B5
x%5E2=4%2B5=9
x=3 and x=-3
The intersection points are then
(3,4), (-3,4), and (0,-5)