Hi Deepak,

The first thing I would do is eliminate the fractions in the first equation. Multiply both des of

\[\frac{8}{x} - \frac{10}{y} = 1\]

by $xy$ to get

\[xy \times \frac{8}{x} - xy \times \frac{10}{y} = xy \mbox{ or } 8y - 10x = xy.\]

Now solve the second equation, $x + y = 9$ for $y$ and substitute into $8y - 10x = xy.$ This will give you a quadratic in $x$ which you can solve.

Once you have solved for $x$ and $y$ substitute into the original equations to verify your answer.

Penny