SOLUTION: How do you workout the problem x^2+9y^2=9 -2x+1y=-3 by elimination method

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Question 749517: How do you workout the problem x^2+9y^2=9
-2x+1y=-3 by elimination method
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
x^2+9y^2=9
-2x+1y=-3 --> y = 2x-3
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Sub for y in the 1st eqn
x^2+9y^2=9
x%5E2+%2B+9%2A%282x-3%29%5E2+=+9
x%5E2+%2B+36x%5E2+-+108x+%2B+81+=+9
37x%5E2+-+108x+%2B+72+=+0
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 37x%5E2%2B-108x%2B72+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-108%29%5E2-4%2A37%2A72=1008.

Discriminant d=1008 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--108%2B-sqrt%28+1008+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-108%29%2Bsqrt%28+1008+%29%29%2F2%5C37+=+1.88850021260507
x%5B2%5D+=+%28-%28-108%29-sqrt%28+1008+%29%29%2F2%5C37+=+1.03041870631385

Quadratic expression 37x%5E2%2B-108x%2B72 can be factored:
37x%5E2%2B-108x%2B72+=+%28x-1.88850021260507%29%2A%28x-1.03041870631385%29
Again, the answer is: 1.88850021260507, 1.03041870631385. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+37%2Ax%5E2%2B-108%2Ax%2B72+%29

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It might be called "elimination" since the y terms were eliminated by the substitution.