Question

Solve: $\frac{2}{x}+\frac{3}{y}=13$, $\frac{5}{x}+\frac{7}{y}=31$

Answer 1

let $\frac{1}{x}=p,\frac{1}{y}=q$

now $2p+3q=13$........1

$5p+7q=31$........2

multiply equation 1 with 5 and 2 with 2

we get $10p+15q=65,10p+14q=62$

subtract equation 1 from 2 equations

we get $q=3\Rightarrow y=\frac{1}{3}$

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

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