SOLUTION: solve simalteneously for x and y: x-y=3 2x^2-3xy+2y(y+1)=3x+13

Question 726720: solve simalteneously for x and y:
x-y=3
2x^2-3xy+2y(y+1)=3x+13

Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
2x^2-3xy+2y(y+1)=3x+13
x-y=3 --> y = x-3
Sub for y in the 1st eqn'
---------
2x^2-3x(x-3) +2(x-3)*(x-2) = 3x+13

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=20 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 4.23606797749979, -0.23606797749979. Here's your graph:

=====================
x = sqrt(5) + 2, y = sqrt(5) - 1
x =~ 4.236, y = 1.236
------------------------
x = 2 - sqrt(5), y = -1 - sqrt(5)
x =~ -0.236, y = -3.236

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