# How do you solve the following linear system  -2x+y=5, -x + 3y - 2z = 0, 4x - 2y + 7z = 3 ?

Jun 9, 2018

$x = - \frac{79}{35} , y = \frac{17}{35} , z = \frac{13}{7}$

#### Explanation:

Multiplying the second equation by $7$ and the third equation by $2$ and adding them:
$x + 17 y = 6$
multiplying this equation by $2$ and adding to the first one:
$y = \frac{17}{35}$
so we get
$- 2 x + \frac{17}{35} = 5$
we obtain
$y = - \frac{79}{35}$
and
$\frac{79}{35} + 3 \cdot \frac{17}{35} = 2 z$

so $z = \frac{13}{7}$