Question

Solve for x and y. $\frac{10}{x+y}+\frac{2}{x-y}=4$ $\frac{15}{x+y}-\frac{5}{x-y}=-2$

Answer 1

$\frac{10}{x+y}+\frac{2}{x-y}=4$

$\frac{15}{x+y}-\frac{5}{x-y}=-2$

let $\frac{1}{x+y}=p$ and $\frac{1}{x-y}=q$

$\Rightarrow 10p+2q=4---\left(1\right)$

$15p-5q=-2---\left(2\right)$

Equation $\left(1\right)\times 5$ and Equation $\left(2\right)\times 2$

$\Rightarrow \frac{50p+10q=2030p-10q=-4}{80p=16}$

$\Rightarrow p=\frac{1}{5}=\frac{1}{x+y}\Rightarrow x+y=5----\left(3\right)$

From $\left(1\right)2q=4-10p=4-2$

$\Rightarrow 2q=2$

$\Rightarrow q=1=\frac{1}{x-y}\Rightarrow x-y=1----\left(4\right)$

$\left(3\right)+\left(4\right)$

$\Rightarrow 2x=6\Rightarrow x=3$

$y=5-x=5-3=2$

$\Rightarrow x=3$ and $y=2$