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 Question from Deepak: This is too complicated please help me 8/x - 10/y = 1 and x+y=9

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

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