# How do you solve using gaussian elimination or gauss-jordan elimination, 2x-3y+z=1, x-2y+3z=2, 3x-4y-z=1?

Apr 6, 2016

The given set of equations is inconsistent; there is no solution

#### Explanation:

Given the equations (re-ordered so first equation has a coefficient of $1$ for $x$
$\textcolor{w h i t e}{\text{XX"){(x-2y+3=2),(2x-3y+z=1),(3x-4y-z=1):}color(white)("XXX}} \left.\begin{matrix}\left[1\right] \\ \left[2\right] \\ \left[3\right]\end{matrix}\right.$

Subtracting $2 \times$[1] from equation [2]
and $3 \times$[1] from equation [3]
$\textcolor{w h i t e}{\text{XX"){(x-2y+3=2),(0x+1y-5z=-3),(0x+2y-10z=-5):}color(white)("XXX}} \left.\begin{matrix}\left[1\right] \\ \left[4\right] \\ \left[5\right]\end{matrix}\right.$

Subtracting $2 \times$[4] from equation [5]
$\textcolor{w h i t e}{\text{XX"){(x-2y+3=2),(0x+1y-5z=-3),(0x+0y+0z=1):}color(white)("XXX}} \left.\begin{matrix}\left[1\right] \\ \left[4\right] \\ \left[6\right]\end{matrix}\right.$

Since [6] is impossible
$\textcolor{w h i t e}{\text{XXX}}$the given equations are inconsistent.