Question

Solve the following systems of equations:
$\frac{5}{x+y}-\frac{2}{x-y}=-1$
$\frac{15}{x+y}+\frac{7}{x-y}=10$

Answer 1

Let $x+y=u,x-y=v$

Rewriting the equations :

Equation (1) : $\frac{5}{u}-\frac{2}{v}=-1$

Equation (2) : $\frac{15}{u}+\frac{7}{v}=10$

Multiply equation (1) by 3 and subtract the resultant equation from equation (2)

$\Rightarrow \frac{15}{u}-\frac{6}{v}=-3$

$\Rightarrow \frac{15}{u}+\frac{7}{v}=10$

$\Rightarrow \frac{13}{v}=13$

$\Rightarrow v=1$

Substituting 'u' in above equations, we get ;

$\Rightarrow u=5$

$\Rightarrow x+y=5$

$\Rightarrow x-y=1$

$\Rightarrow 2x=6$

$\Rightarrow x=3$

And $y=2$