Question

Solve the following systems of equations:
$\frac{44}{x+y}+\frac{30}{x-y}=10$
$\frac{55}{x+y}+\frac{40}{x-y}=13$

Answer 1

Equation (1) ×$4$ : $\frac{176}{x+y}+\frac{120}{x-y}=40$

Equation (2) ×$3$ : $\frac{165}{x+y}+\frac{120}{x-y}=39$

Subtract two equations ;

$\Rightarrow \frac{11}{x+y}=1$

$\Rightarrow x+y=11$

Substituting, we get ;

$\Rightarrow x-y=5$

Adding resultant equations ;

$\Rightarrow 2x=16$

$\Rightarrow x=8$

$\Rightarrow y=3$