Question

Solve the following system of equation:
$\frac{1}{2x}-\frac{1}{y}=-1$
$\frac{1}{x}+\frac{1}{2y}=8$ ,where x $\ne$ 0, y $\ne$ 0.

Answer 1

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

$=>\frac{1}{2x}+1=\frac{1}{y}$

$=>\frac{1+2x}{2x}=\frac{1}{y}$

$=>y=\frac{2x}{2x+1}\frac{1}{x}+\frac{1}{2y}=8$

$=>\frac{1}{x}-8=-\frac{1}{2y}$

$=>\frac{1-8x}{x}=-\frac{1}{2}\times \frac{2x+1}{2x}$

$=>4-32x=-2x-1$$=>30x=5$

$=>x=\frac{1}{6}y=\frac{2\times \frac{1}{6}}{2\times \frac{1}{6}+1}=\frac{\frac{1}{3}}{\frac{1}{3}+1}=\frac{1}{3}\times \frac{3}{4}$

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