Question

Solve $\frac{1}{x}-\frac{4}{y}=2,\frac{1}{x}-\frac{3}{y}=9$ by reducing it into the pair of linear equations

Answer 1

$\frac{1}{x}-\frac{4}{y}=2,\frac{1}{x}-\frac{3}{y}=9$

Let $\frac{1}{x}=u$ and $\frac{1}{y}=v$

then we have

$u-4v=2-\left(i\right)u-3v=9-\left(ii\right)$

Subtracting eq.$\left(ii\right)$ from $\left(i\right)$

$v=7$

Also, $u-3\times 7=9\Rightarrow u=21+9=30$

Now, $v=\frac{1}{y}\Rightarrow y=\frac{1}{v}=\frac{1}{7}$

and $u=\frac{1}{x}\Rightarrow x=\frac{1}{u}=\frac{1}{21}$