Question 647926
The system

2x-3y+z=5
x+3y+8z=22
3x-y+2z=12


converts to the matrix


<img src="http://latex.codecogs.com/gif.latex?\LARGE \begin{bmatrix} 2 & -3 & 1 & 5\\ 1 & 3 & 8 & 22\\ 3 & -1 & 2 & 12 \end{bmatrix}" title="\LARGE \begin{bmatrix} 2 & -3 & 1 & 5\\ 1 & 3 & 8 & 22\\ 3 & -1 & 2 & 12 \end{bmatrix}" />


Now row reduce to get 

(Solution provided by the <a href="http://www.math.odu.edu/~bogacki/lat/">Linear Algebra Toolkit</a>)

<img src="http://i150.photobucket.com/albums/s91/jim_thompson5910/Algebra%20dot%20com/9-8-20129-25-03PM.png">

(Solution provided by the <a href="http://www.math.odu.edu/~bogacki/lat/">Linear Algebra Toolkit</a>)


So the solutions are 


{{{x = 3}}}, {{{y = 1}}}, and {{{z = 2}}}