Question

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

Answer 1

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

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

Subtract two equations ;

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

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

Substitute y in equation 1 ;

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