Question

Solve for x and y : $\frac{xy}{x+y}$ = $\frac{1}{5}$ , $\frac{xy}{x-y}$ = $\frac{1}{7}$ : x + y $\ne$ 0 and x $\ne$ y

Answer 1

Given that

$\frac{xy}{x+y}=\frac{1}{5},\frac{xy}{x-y}=\frac{1}{7}$

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

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

$x+y=5xy$

$x-y=7xy$

$\overline{2x=12xy}$

$y=\frac{2x}{12x}\Rightarrow y=\frac{1}{6}$

$y=\frac{1}{6}$ Put in value equation 1st

$x+y=5xy$

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

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

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

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

$x=-1$

$\left(x=-1,+y=\frac{1}{6}\right)$