Question 645151
2w-x+5y+z=-3
3w+2x+2y-6z=-32
w+3x+3y-z=-47
5w-2x-3y+3z=49 


translates to the matrix


<img src="http://latex.codecogs.com/gif.latex?\LARGE \begin{bmatrix} 2 & -1 & 5 & 1 & -3\\ 3 & 2 & 2 & -6 & -32\\ 1 & 3 & 3 & -1 & -47\\ 5 & -2 & -3 & 3 & 49 \end{bmatrix}" title="\LARGE \begin{bmatrix} 2 & -1 & 5 & 1 & -3\\ 3 & 2 & 2 & -6 & -32\\ 1 & 3 & 3 & -1 & -47\\ 5 & -2 & -3 & 3 & 49 \end{bmatrix}" />


Now use row reduction 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/9-3-20125-48-14PM.png">

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



So the solutions are 


{{{w = 2}}}, {{{x = -12}}}, {{{y = -4}}}, {{{z = 1}}}