Question

Solve the following systems of equations:
$x+y=2xy$
$\frac{x-y}{xy}=6$
$x\ne 0,y\ne 0$

Answer 1

Divide 1st equation by 'xy' ;

Equation (1) : $\frac{1}{x}+\frac{1}{y}=2$

Equation (2) : $\frac{1}{x}-\frac{1}{y}=-6$

Adding both, we get ;

$\Rightarrow \frac{2}{x}=-4$

$\Rightarrow x=\frac{-1}{2}$

Substituting in either equation, we get ;

$\Rightarrow y=\frac{1}{4}$