# How do you solve using gaussian elimination or gauss-jordan elimination, x-2y+z=-14, y-2z=7, 2x+3y-z=-1?

Dec 20, 2017

$x = \frac{80}{7}$, $y = - \frac{345}{7}$ and $z = - 124$

#### Explanation:

From $x - 2 y + z = - 14$, $z = 2 y - x - 14$

Hence $y - 2 \cdot \left(2 y - x - 14\right) = 7$ or $2 x - 3 y = - 35$ $\left(a\right)$ and,

$2 x + 3 y - \left(2 y - x - 14\right) = - 1$ or $3 x + y = - 15$ $\left(b\right)$

$3 x + y = - 15$, $y = - 3 x - 15$

Consequently, $2 x - 3 \cdot \left(- 3 x - 15\right) = - 35$ and $- 7 x = - 80$, so $x = \frac{80}{7}$

Thus, $y = - 3 \cdot \frac{80}{7} - 15 = - \frac{345}{7}$ and $z = 2 \cdot \left(- \frac{345}{7}\right) - \frac{80}{7} - 14 = - 124$