SOLUTION: Solve 9-x^2=y^2, x+y=3, as a linear simultaneous question.

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Question 700155: Solve 9-x^2=y^2, x+y=3, as a linear simultaneous question.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
THE ALGEBRA:
system%289-x%5E2=y%5E2%2C+x%2By=3%29 --> system%289-x%5E2=y%5E2%2C+y=3-x%29 --> 9-x%5E2=%283-x%29%5E2 --> 9-x%5E2=9-6x%2Bx%5E2 --> 2x%5E2-6x=0 --> 2x%28x-3%29=0
The solutions are
system%28x=0%2C+y=3-x%29 --> system%28x=0%2C+y=3%29 for point (0,3) and
system%28x-3=0%2C+y=3-x%29 --> system%28x=3%2C+y=3-x%29 --> system%28x=3%2C+y=3-3%29 --> system%28x=3%2C+y=0%29 for point (3,0).

THE GEOMETRY:
9-x%5E2=y%5E2 --> x%5E2%2By%5E2=9 represents a circle of radius 3, centered at the origin.
x%2By=3 represents a line with intercepts at (0,3) and (3,0),
which are points on the circle,
and solutions to the problem.
graph%28300%2C300%2C-5%2C5%2C-5%2C5%2Csqrt%289-x%5E2%29%2C-sqrt%289-x%5E2%29%2C3-x%29