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

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Question 1075210: 3x + 2y=10
3/x + 2/y = 5
Answer by Alan3354(69443) About Me  (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
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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 ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B-11x%2B6+=+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=%28-11%29%5E2-4%2A2%2A6=73.

Discriminant d=73 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--11%2B-sqrt%28+73+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-11%29%2Bsqrt%28+73+%29%29%2F2%5C2+=+4.88600093632938
x%5B2%5D+=+%28-%28-11%29-sqrt%28+73+%29%29%2F2%5C2+=+0.613999063670617

Quadratic expression 2x%5E2%2B-11x%2B6 can be factored:
2x%5E2%2B-11x%2B6+=+%28x-4.88600093632938%29%2A%28x-0.613999063670617%29
Again, the answer is: 4.88600093632938, 0.613999063670617. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-11%2Ax%2B6+%29

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