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Question
Solve the following systems of equations:
`x+y = 2xy`
`(x - y)/(xy) = 6` x != 0, y != 0
Solution
The system of the given equation is
x + y = 2xy .....(i)
And `(x - y)/(xy) = 6`
x - y = 6xy .....(ii)
Adding equation (i) and equation (ii), we get
2x = 2xy + 6xy
=> 2x = 8xy
`=> (2x)/(8x) = y`
`=> y = 1/4`
Putting y = 1/4 in equation (i) we get
`x + 1/4 = 2x xx 1/4`
`=> x + 1/4 = x/2`
`=> x - x/2 = (-1)/4`
`=> (2x - x)/2 = (-1)/4`
`=> x = (-2)/4 = (-1)/2`
Hence, solution of the given system of equation is `x = (-1)/2, y = 1/4`
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