Question

Solve :
$\frac{7x-2y}{xy}=5$
$\frac{8x+7y}{xy}=15$

Answer 1

$\frac{7x-2y}{xy}=5⟹\frac{7}{y}-\frac{2}{x}=5\cdots \left(1\right)$

$\frac{8x+7y}{xy}=15⟹\frac{8}{y}+\frac{7}{x}=15\cdots \left(2\right)$

$\left(1\right)\times 7⟹\frac{49}{y}-\frac{14}{x}=35\cdots \left(3\right)$

$\left(2\right)\times 2⟹\frac{16}{y}-\frac{14}{x}=30\cdots \left(4\right)$

$\left(3\right)+\left(4\right)⟹\frac{65}{y}=65⟹y=1$

Put $y=1$ in $\left(1\right)$

$\frac{7}{1}-\frac{2}{x}=5⟹\frac{2}{x}=2⟹x=1$