# 3/x+2/y=2 2/x+3/y=1/4

Solve the simultaneous equation:

`3/x+2/y=2`

`2/x+3/y=1/4`

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Multiply the first equation by -2 and the second equation by 3 to get:

`-6/x-4/y=-4`

`5/y=-13/4`   Take the reciprocal of both sides (a property of proportions)

`y/5=-4/13`  Multiply both sides by 5:

`y=-20/13`

Substitute into the first equation:

`3/x+2/(-20/13)=2`

`3/x-26/20=2`  Add `26/20` to both sides:

`3/x=33/10`  Take the reciprocal of both sides:

`x/3=10/33`  Multiply both sides by 3:

`x=30/33=10/11`

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The solution is `(10/11,-20/13)`

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The graph:

Note that the graph shows (0,0) as a solution, but it is not in the domain of the original problem.

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