SOLUTION: 3x + 2y=10 3/x + 2/y = 5

Question 1075210: 3x + 2y=10
3/x + 2/y = 5
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
3x + 2y=10 --> y = 5 - 3x/2
3/x + 2/y = 5 --> 2x + 3y = 5xy
===============
2x + 3y = 5xy
Sub for y
2x + 15 - 9x/2 = 5x*(5 - 2x/2) = 25x - 10x^2/2
2x + 15 - 9x/2 = 25x - 10x^2/2
4x + 30 - 9x = 50x - 10x^2
10x^2 - 55x + 30 = 0
2x^2 - 11x + 6 = 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=73 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 4.88600093632938, 0.613999063670617. Here's your graph:

=========================
x =~ 4.886
y =~ -2.329
==================
x =~ 0.614
You can solve for y.

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