# How do you solve using gaussian elimination or gauss-jordan elimination, x+2y-z=-5, 3x+2y+3z=-7, 5x-y-2z=-30?

$x = - 5$
$y = 1$
$z = 2$

#### Explanation:

Gaussian Elimination or Gauss-Jordan elimination

$\left[\begin{matrix}1 & 2 & - 1 & | & - 5 \\ 3 & 2 & 3 & | & - 7 \\ 5 & - 1 & - 2 & | & - 30\end{matrix}\right]$

$\left[\begin{matrix}1 & 2 & - 1 & | & - 5 \\ 0 & - 4 & 6 & | & 8 \\ 0 & - 11 & 3 & | & - 5\end{matrix}\right]$

$\left[\begin{matrix}1 & 2 & - 1 & | & - 5 \\ 0 & - 2 & 3 & | & 4 \\ 0 & - 11 & 3 & | & - 5\end{matrix}\right]$

$\left[\begin{matrix}1 & 2 & - 1 & | & - 5 \\ 0 & - 2 & 3 & | & 4 \\ 0 & - 1 & - 12 & | & - 25\end{matrix}\right]$

$\left[\begin{matrix}1 & 2 & - 1 & | & - 5 \\ 0 & 1 & 39 & | & 79 \\ 0 & - 1 & - 12 & | & - 25\end{matrix}\right]$

$\left[\begin{matrix}1 & 0 & - 79 & | & - 163 \\ 0 & 1 & 39 & | & 79 \\ 0 & 0 & 27 & | & 54\end{matrix}\right]$

$\left[\begin{matrix}1 & 0 & 0 & | & - 5 \\ 0 & 1 & 0 & | & 1 \\ 0 & 0 & 1 & | & 2\end{matrix}\right]$

$x = - 5$
$y = 1$
$z = 2$

God bless....I hope the explanation is useful.