Question

Solve the following systems of equations:
$\frac{22}{x+y}+\frac{15}{x-y}=5$
$\frac{55}{x+y}+\frac{45}{x-y}=14$

Answer 1

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

Rewriting the equations :

Equation (1) : $\frac{22}{u}+\frac{15}{v}=5$

Equation (2) : $\frac{55}{u}+\frac{45}{v}=14$

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

$\Rightarrow \frac{66}{u}+\frac{45}{v}=15$

$\Rightarrow \frac{55}{u}+\frac{45}{v}=14$

$\Rightarrow \frac{11}{u}=1$

$\Rightarrow u=11$

Substituting 'u' in above equations, we get ;

$\Rightarrow v=5$

$\Rightarrow x+y=11$

$\Rightarrow x-y=5$

$\Rightarrow 2x=16$

$\Rightarrow x=8$

And $y=3$