Question

Solve the following pair of equation$\frac{15}{x-y}+\frac{22}{x+y}=5$; $\frac{40}{x-y}+\frac{55}{x+y}=13$ (where $x\ne y$; $x\ne y$)

Answer 1

Put $\frac{5}{x-y}=h,\frac{11}{x+y}=k$

$⟹$ equations are $3h+2k=5,8h+5k=13$

On solving we get $h=1,k=1⟹x-y=\mathrm{5....}\left(1\right),x+y=\mathrm{11....}\left(2\right)$

$\left(1\right)+\left(2\right)⟹2x=16⟹x=8$

$\left(1\right)-\left(2\right)⟹-2y=-6⟹y=3$