Solve the following systems of the equation:

X+Y=2XY, X-Y/XY=6

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Solution

X+Y=2XY (1)
X-Y/XY=6
X- Y = 6XY (2)
Adding (1) and (2) 2X = 8XY
Dividing by X (as X can't be 0) we get
2= 8Y or Y = 1/4
Subtracting (2) from (1), 2Y = -4XY
Dividing by Y(Y can't be 0)
2 = -4X or X = -1/2
Answer X = -1/2 and Y = 1/4

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