SOLUTION: Solve the following system. x2 + y 2= 25 2x + y = 10 The solution set {(-, ), (, )}.

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Solve the following system. x2 + y 2= 25 2x + y = 10 The solution set {(-, ), (, )}.       Log On


   

Question 300288: Solve the following system.
x2 + y 2= 25
2x + y = 10
The solution set {(-, ), (, )}.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The solution to this system solves the intersection of a circle and a line.

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.
.
1.x%5E2%2By%5E2=25
2.2x%2By=10
From eq. 2,
y=-2x%2B10
y%5E2=%28-2x%2B10%29%5E2
y%5E2=4x%5E2-40x%2B100
Substitute into eq. 1,
x%5E2%2By%5E2=25
x%5E2%2B4x%5E2-40x%2B100=25
5x%5E2-40x%2B100=25
5x%5E2-40x%2B75=0
x%5E2-8x%2B15=0
Factor,
%28x-3%29%28x-5%29=0
Two solutions:
x-3=0
x=3
Then using eq. 2,
+2x%2By=10
6%2By=10
y=4
(3,4)
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.
.
x-5=0
x=5
10%2By=10+
y=0
(5,0)
The solution is verified by the previous graph.