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Question

Solve: 3x+y+2xy and 9x+y4xy=1

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Solution

3x+y+2xy=1....(1)
9x+y4xy=1....(2)

3(xy)+2(x+y)=(x+y)(xy)
3x3y+2x+2y=x2y2
5xy=x2y2....(3)

9(xy)4(x+y)=(x+y)(xy)
9x9y4x4y=x2y2
5x13y=x2y2...(4)

subtracting equation (4) and (3)
5xy=x2y2
5x13y=x2y2
we get
12y=0
y=0
put in equation (3)
5x0=x20
5x=x2
x=5


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