Question

Solve for $x$ and $y$

$\frac{2}{x}+\frac{3}{y}=\frac{9}{xy}$ and $\frac{4}{x}+\frac{9}{y}=\frac{21}{xy}$

Answer 1

$\frac{2}{x}+\frac{3}{y}=\frac{4}{xy}$ ------- (1)

$\frac{4}{x}+\frac{9}{y}=\frac{21}{xy}$ ------ (2)

on multiplying equation (1) by 2 & then subtract from equation (2) we get

$\frac{4}{x}+\frac{9}{y}=\frac{21}{xy}$

$\frac{4}{x}+\frac{6}{y}=\frac{18}{xy}$

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$\frac{3}{y}=\frac{3}{xy}$

[x=1] noe from equation (1)

$\frac{2}{x}+\frac{3}{y}=\frac{9}{xy}$

$\frac{9}{y}-\frac{3}{y}=2\Rightarrow y=\frac{6}{2}=3$

Hence [x=1] and [y=3]