SOLUTION: Solve the nonlinear system by substitution: {{{x^2+y^2=10 -3X+Y=0}}}

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Question 92298: Solve the nonlinear system by substitution:
x%5E2%2By%5E2=10%0D%0A++-3X%2BY=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I assume it looks like this right?
x%5E2%2By%5E2=10
-3x%2By=0


y=3x Solve the 2nd equation for y

x%5E2%2B%283x%29%5E2=10 Plug in y=3x

x%5E2%2B9x%5E2=10 Square 3x to get 9x%5E2

x%5E2%2B9x%5E2-10=0 Subtract 10 from both sides


10x%5E2-10=0 Combine like terms

10%28x%5E2-1%29=0 Factor out 10

x%5E2-1=0 Set each factor equal to zero

x%5E2=1 Add one to both sides

Take the square root of both sides


So the solution breaks down to:

x=1 or x=-1







Now plug in x=1 to find y

y=3%281%29=3

So when x=1, y=3


Now plug in x=-1 to find y

y=3%28-1%29=-3

So when x=-1, y=-3



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Answer:
So our solutions are

x=1 and y=3 which makes the point (1,3)


and


x=-1 and y=-3 which makes the point (-1, -3)