Question
Solve :$\frac{9}{x}-\frac{4}{y}=8; \frac{13}{x}+\frac{7}{y}=101$

Answer

$\frac{9}{x}-\frac{4}{y}=8\ldots .(1)$
$\frac{13}{x}+\frac{7}{y}=101\ldots . .(2)$
Multiplying equation no. $(1)$ by $7$ and $(2)$ by $4 .$
$\frac{63}{x}-\frac{28}{y}=56\ldots . .(3)$
$\frac{52}{x}+\frac{28}{y}=404\ldots . . .(4)$
Adding equation $(3)$ and $(4)$
$\frac{63}{x}-\frac{28}{y}=56$
$+\frac{52}{x}+\frac{28}{y}=404$
$\frac{115}{x}=460$
$x=\frac{115}{460}=x=\frac{1}{4}$
From $(1)$
$9 \times\left(\frac{4}{1}\right)-\frac{4}{y}=8$
$ -\frac{4}{y}=-28$
$ y=\frac{1}{7}$

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