Question

Solve: $\frac{20}{x+y}+\frac{3}{x-y}=7$, $\frac{8}{x-y}-\frac{15}{x+y}=5$

Answer 1

Let $\frac{1}{x+y}=u\frac{1}{x-y}=v$

$204+3v=7$ and $8v-15u=5$

$24v+160\mu =56$

$24v-45\mu =15$

$-$ $+$ $-$

$\overline{205\mu =41}$

$u=\frac{41}{205}=\frac{1}{5}$

$v=1$

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

$x+y=5$

$x-y=1$

$\overline{2x=6}$

$x=3$

$y=2$