Question

Solve the following systems of equations:

`x+y = 2xy`

`(x - y)/(xy) = 6`   x != 0, y != 0

Answer 1

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`