SOLUTION: can you sovle the system x^2=25-y^2 and xy=-12 algebarically?

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Question 435200: can you sovle the system x^2=25-y^2 and xy=-12 algebarically?
Answer by Gogonati(855) About Me  (Show Source):
You can put this solution on YOUR website!
To solve system%28x%5E2%2By%5E2=25%2C+x%2Ay=-12%29, first we make some identical
transformations in the first equation.
x%5E2%2By%5E2%2B2xy=25%2B2xy => %28x%2By%29%5E2=25%2B2%28-12%29 => x%2By=1 and
x%2By=-1, now we need to solve two other simplest systems:
system%28x%2By=1%2C+x%2Ay=-12%29 and system%28x%2By=-1%2C+x%2Ay=-12%29.
We solve these systems by substitution:1) y=1-x and x(1-x)=-12 =>-x^2+x+12=0, where x=4 and x=-3.
Plug in x=4 we get y=-3 and plug in x=-3 we get y=4
We got two solution: (4, -3) and (-3, 4)
2)y=-x-1 and x(-x-1)=-12 => -x^2-x+12=0, where x=3 and x=-4
Plug in x=3 we get y=-4 and plug in x=-4 we get y=3 and we get two other solutions: (3, -4) and (-4, 3). Summarize the results we :
Answer:The solution are the points: (4, -3), (-3, 4), (3, -4) and ( -4, 3).