Question

Solve the following systems of equations:
$\frac{10}{x+y}+\frac{2}{x-y}=4$
$\frac{15}{x+y}-\frac{9}{x-y}=-2$

Answer 1

Equation (1) ×3 : $\frac{30}{x+y}+\frac{6}{x-y}=12$

Equation (2) ×2 : $\frac{30}{x+y}-\frac{18}{x-y}=-4$

Subtract two equations ;

$\Rightarrow \frac{24}{x-y}=16$

$\Rightarrow x-y=\frac{3}{2}$

Substituting, we get ;

$\Rightarrow x+y=\frac{15}{4}$

Adding resultant equations;

$\Rightarrow 2x=\frac{21}{4}$

$\Rightarrow x=\frac{21}{8}$

Substituting 'x' in the above equations, we get ;

$\Rightarrow y=\frac{9}{8}$