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Solve the following systems of equations:
$x + y = 2 xy,$

$\frac{x - y}{xy} = 6, x \neq 0, y \neq 0$

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x = - \frac{1}{2}, y = 1 / 4

x = \frac{1}{2}, y = 1 / 5

x = \frac{1}{3}, y = - 1 / 4

x = \frac{3}{2}, y = 1 / 2

answer is A.

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Detailed Solution

The given equations are,

x + y = 2 xy \dots (i)

\frac{x - y}{xy} = 6

Or,

x - y = 6 xy \dots (ii)

Add equation (i) and (ii) to get,

2 x = 2 xy + 6 xy

2 x = 8 xy

\frac{2 x}{8 x} = y

y = \frac{1}{4}

Put the value of y in equation (i),

x + \frac{1}{4} = 2 x \times \frac{1}{4}

x + \frac{1}{4} = \frac{x}{2}

x - \frac{x}{2} = \frac{- 1}{4}

\frac{2 x - x}{2} = \frac{- 1}{4}

x = \frac{- 2}{4} = \frac{- 1}{2}

As a result, the given equation system's solution is

x = - \frac{1}{2}, y = 1 / 4

Option 1 is correct.

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