# How do you solve the following system?: 11x -23y =-13 , -23x +17y = 8

Dec 29, 2015

Reorder one of the equations to express y in terms of x, and then substitute into the other equation and resolve for x. Substitute this value for x back into the first equation and evaluate for y.

#### Explanation:

$17 y = 8 + 23 x$
$y = \frac{8 + 23 x}{17}$
$11 x - 23 \cdot \frac{8 + 23 x}{17} = - 13$
$11 x - 184 - 589 x = - 221$
$578 x = 37$
$x = \frac{37}{578} \implies 0.064$
$17 y = 8 + 23 \cdot \frac{37}{578}$
$y = \frac{4624 + 851}{578 \cdot 17} = \frac{5475}{9826} \implies 0.557$