# Question #871eb

Dec 4, 2017

$x = \frac{2}{13}$, $y = - \frac{1}{5}$

#### Explanation:

Equations are:

(1) $\frac{2}{x} + \frac{3}{y} = - 2$
(2) $\frac{4}{x} + \frac{5}{y} = 1$

Multiply each equation by $x y$ to get:

(1) $2 y + 3 x = - 2 x y$
(2) $4 y + 5 x = x y$

Now balance the $y$ terms:

(1) $4 y + 6 x = - 4 x y$
(2) $4 y + 5 x = x y$

Subtract (2) from (1):

$x = - 5 x y$

Cancel the $x$ terms and solve for $y$:

$1 = - 5 y$

$y = - \frac{1}{5}$

Now sub $- \frac{1}{5}$ back into equation (1) and solve for $x$, which comes out to be $\frac{2}{13}$