SOLUTION: How would you solve this problem by substitution? x^2+y^2=9 x+y=3

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Question 89697: How would you solve this problem by substitution?
x^2+y^2=9
x+y=3

Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2%2By%5E2=9
x%2By=3

x%5E2%2By%5E2=9
y=3-x Subtract x from both sides


x%5E2%2B%283-x%29%5E2=9 Plug in y=3-x


x%5E2%2B9-6x%2Bx%5E2=9 Foil


x%5E2%2B9-6x%2Bx%5E2-9=0 Subtract 9 from both sides


2x%5E2-6x=0 Combine like terms

2x%28x-3%29=0 Factor out 2x

2x=0 or x-3=0 Set each factor equal to x

x=0 or x=3 Solve for x

So we have x values x=0 or x=3

Lets find y with x=0

y=3-0=3

So one solution is (0,3)


Lets find y with x=3

y=3-3=0

So another solution is (3,0)


Here's some visual proof
drawing%28+900%2C+900%2C+-10%2C+10%2C+-10%2C+10%2C%0D%0A+++++++++grid%281%29%2C%0D%0A+++++++++circle%280%2C0%2C3%29%2C%0D%0A+++++++++graph%28+900%2C+900%2C+-10%2C+10%2C+-10%2C+10%2C3-x%29%2C%0D%0A+++++++++blue%28circle%283%2C0%2C0.05%29%29%2C%0D%0A+++++++++blue%28circle%283%2C0%2C0.08%29%29%2C%0D%0A+++++++++green%28circle%280%2C3%2C0.05%29%29%2C%0D%0A+++++++++green%28circle%280%2C3%2C0.08%29%29%0D%0A%29 graph of x%5E2%2By%5E2=9 and x%2By=3

Here we can see that the intersections are (0,3) and (3,0). So this verifies our answer.