Question

Solve the following systems of equations:
$\frac{1}{2x}+\frac{1}{3y}=2$
$\frac{1}{3x}+\frac{1}{2y}=\frac{13}{6}$

Answer 1

Equation (1)$\times \frac{1}{3}:\frac{1}{6x}+\frac{1}{9y}=\frac{2}{3}$........1

Equation (2)$\times \frac{1}{2}:\frac{1}{6x}+\frac{1}{4y}=\frac{13}{12}$....2

Subtract two equations ;

$\Rightarrow \frac{-5}{36y}=\frac{-5}{12}$

$\Rightarrow y=\frac{1}{3}$

Substitute y in equation 1 ;

$\Rightarrow x=\frac{1}{2}$