SOLUTION: Solve by substitution method x-2y=2... X^2+y^2-2x+3y=4

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Question 1067967: Solve by substitution method x-2y=2...
X^2+y^2-2x+3y=4
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
x-2y=2 --> x = 2y+2
X^2 + y^2 - 2x + 3y = 4
Sub for x
(2y+2)^2 + y^2 - 2(2y+2) + 3y = 4
4y^2 + 8y + 4 + y^2 - 4y - 4 + 3y = 4
5y^2 + 7y - 4 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 5x%5E2%2B7x%2B-4+=+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=%287%29%5E2-4%2A5%2A-4=129.

Discriminant d=129 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-7%2B-sqrt%28+129+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%287%29%2Bsqrt%28+129+%29%29%2F2%5C5+=+0.435781669160055
x%5B2%5D+=+%28-%287%29-sqrt%28+129+%29%29%2F2%5C5+=+-1.83578166916005

Quadratic expression 5x%5E2%2B7x%2B-4 can be factored:
5x%5E2%2B7x%2B-4+=+%28x-0.435781669160055%29%2A%28x--1.83578166916005%29
Again, the answer is: 0.435781669160055, -1.83578166916005. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B7%2Ax%2B-4+%29

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y = -7%2F10+%2B+sqrt%28129%29%2F10
x = 3%2F5+%2B+sqrt%28129%29%2F5
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y = -7%2F10+-+sqrt%28129%29%2F10
x = 3%2F5+-+sqrt%28129%29%2F5