Question

Solve the following systems of equations:
$\frac{1}{5x}+\frac{1}{6y}=12$
$\frac{1}{3x}-\frac{3}{7y}=8,x\ne 0,y\ne 0$

Answer 1

Equation (1)$\times 15:\frac{3}{x}+\frac{15}{6y}=180$

Equation (2)$\times 9:\frac{3}{x}-\frac{27}{7y}=72$

Subtract two equations ;

$\Rightarrow \frac{89}{14y}=108$

$\Rightarrow y=\frac{89}{1512}$

Substitute y in equation 1 ;

$\Rightarrow x=\frac{89}{4080}$