# How do you solve 3/x +2/y = - 5/6 and 1/x - 1/y = -5/6 using substitution?

Jan 9, 2018

$x = - 2$ and $y = 3$

#### Explanation:

As $\frac{1}{x} - \frac{1}{y} = - \frac{5}{6}$, we have $\frac{1}{x} = \frac{1}{y} - \frac{5}{6}$

substituting $\frac{1}{x}$ in first equation we get

$3 \left(\frac{1}{y} - \frac{5}{6}\right) + \frac{2}{y} = - \frac{5}{6}$

or $\frac{3}{y} - \frac{15}{6} + \frac{2}{y} = - \frac{5}{6}$

or $\frac{5}{y} = \frac{10}{6}$

or$10 y = 30$ and $y = 3$

Hence $\frac{1}{x} = \frac{1}{3} - \frac{5}{6} = \frac{2 - 5}{6} = - \frac{3}{6} = - \frac{1}{2}$

i.e. $x = - 2$