Question

Solve the following systems of equations:
$\frac{2}{3x+2y}+\frac{3}{3x-2y}=\frac{17}{5}$
$\frac{5}{3x+2y}+\frac{1}{3x-2y}=2$

Answer 1

Equation (2) × $3$ : $\frac{15}{3x+2y}+\frac{3}{3x-2y}=6$

Equation (1) : $\frac{2}{3x+2y}+\frac{3}{3x-2y}=\frac{17}{5}$

Subtract two equations ;

$\Rightarrow \frac{13}{3x+2y}=\frac{13}{5}$

$\Rightarrow 3x+2y=5$

$\Rightarrow 3x-2y=1$

Adding both equations ;

$\Rightarrow 6x=6$

$\Rightarrow x=1$

Substituting $x$ in the above equation, we get ;

$\Rightarrow y=1$