# How do solve the following linear system?:  x/2 - y/4 = -1 , 2/3x + 4y = -1 ?

Feb 7, 2016

$x = - \frac{51}{26}$ and $y = \frac{1}{13}$

#### Explanation:

(a) $\frac{x}{2} - \frac{y}{4} = - 1$

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

First eliminate the fractions, multiplying (a) by 4 and (b) by 3:

(a) $2 x - y = - 4$

(b) $2 x + 12 y = - 3$

Do (b)-(a):

$13 y = 1 \implies y = \frac{1}{13}$

For x, replace y in (a)

$2 x - \frac{1}{13} = - 4$
$2 x = - 4 + \frac{1}{13}$
$2 x = - \frac{51}{13}$
$x = - \frac{51}{26}$