Question

Solve for $x$ & $y$ :$\frac{xy}{x+5}=\frac{1}{5}$; $\frac{xy}{x-y}=\frac{1}{7}$

Answer 1

$Giventhat$

$\frac{xy}{x+y}=\frac{1}{5}$

$\Rightarrow x+y=5xy---\left(i\right)$

$And,$

$\frac{xy}{x-y}=\frac{1}{7}$

$\Rightarrow x-y=7xy----\left(ii\right)$

$Adding\left(i\right)and\left(ii\right)weget,$

$x+y=5xy$

$x-y=7xy$

_______________

$2x=12xy$

$\Rightarrow y=\frac{2x}{12x}$

$\therefore y=\frac{1}{6}$

$Now$

$Puty=\frac{1}{6}ineq{u}^n\left(i\right)weget,$

$x+y=5xy$

$\Rightarrow x+\frac{1}{6}=5x\times \frac{1}{6}$

$\Rightarrow x-\frac{5x}{6}=\frac{-1}{6}$

$\Rightarrow \frac{6x-5x}{6}=\frac{-1}{6}\left[cancle6bothside\right]$

$\Rightarrow x=-1$

Hence

$x=-1$

$y=\frac{1}{6}$