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

Question 1067967: Solve by substitution method x-2y=2...
X^2+y^2-2x+3y=4
Answer by Alan3354(69443) (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 (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=129 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 0.435781669160055, -1.83578166916005. Here's your graph:

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y =
x =
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y =
x =

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