# How do you solve the following system:  8x - y = 13 , 5x-9y=-23 ?

Jun 19, 2018

$x = \frac{140}{67} = 2 \frac{6}{67}$
$y = \frac{249}{67} = 3 \frac{48}{67}$

#### Explanation:

System of equations:
1) $8 x - y = 13 \implies y = 8 x - 13$
2) $5 x - 9 y = - 23 \implies 9 y = 5 x + 23$
1) inserted in 2) gives:
3) $9 \left(8 x - 13\right) = 5 x + 23 \implies 72 x - 117 = 5 x + 23$
$67 x = 140 \implies x = \frac{140}{67} = 2 \frac{6}{67}$
Inserted in 1):
$y = 8 \cdot 2 \frac{6}{67} - 13 = 16 \frac{48}{67} - 13 = 3 \frac{48}{67}$

Check: $5 x - 9 y = 5 \cdot 2 \frac{6}{67} - 9 \cdot 3 \frac{48}{67} = - 23$