SOLUTION: How to solve this? 2/x - 3y =1 -4/x + 7/y =1

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Question 378857: How to solve this?
2/x - 3y =1
-4/x + 7/y =1
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
2/x - 3y =1
-4/x + 7/y =1
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Multiply the 1st eqn by 2
4/x - 6y = 2
-4/x + 7/y =1
----------------- Add
-6y + 7/y = 3
Multiply by -y
6y^2 - 7 = -3y
6y^2 + 3y - 7 = 0
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 6x%5E2%2B3x%2B-7+=+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=%283%29%5E2-4%2A6%2A-7=177.

Discriminant d=177 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-3%2B-sqrt%28+177+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%283%29%2Bsqrt%28+177+%29%29%2F2%5C6+=+0.858677891304172
x%5B2%5D+=+%28-%283%29-sqrt%28+177+%29%29%2F2%5C6+=+-1.35867789130417

Quadratic expression 6x%5E2%2B3x%2B-7 can be factored:
6x%5E2%2B3x%2B-7+=+%28x-0.858677891304172%29%2A%28x--1.35867789130417%29
Again, the answer is: 0.858677891304172, -1.35867789130417. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+6%2Ax%5E2%2B3%2Ax%2B-7+%29

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y = (-3 ± sqrt(177))/12 It says x, but it's y)
Sub for y into eqn 1 and find x.