Optional extension

Solve the following pair of simultaneous equations, where $x\ne0$ and $y\ne0$.

$\frac1x-\frac1y=5$

$\frac2x+\frac3y=0$[3]

Question

Optional extension Solve the following pair of simultaneous equations, where $x\ne0$ and $y\ne0$. $\frac1x-\frac1y=5$ $\frac2x+\frac3y=0$

Accepted Answer

$x=\frac13$, $y=-\frac12$.

Reciprocal substitution II