Question 176992
First, extract the coefficients to form the following matrix:



{{{(matrix(3,4,1,-1,1,1,1,1,3,-3,2,-1,2,0))}}}



 Add  -1*Row 1 to Row 2 to get the new Row 2


{{{(matrix(3,4,1,-1,1,1,0,2,2,-4,2,-1,2,0))}}}


 Add  -2*Row 1 to Row 3 to get the new Row 3


{{{(matrix(3,4,1,-1,1,1,0,2,2,-4,0,1,0,-2))}}}


Multiply Row 2 by {{{1/2}}} to make the pivot 1:


{{{(matrix(3,4,1,-1,1,1,0,1,1,-2,0,1,0,-2))}}}


 Add  -1*Row 2 to Row 3 to get the new Row 3


{{{(matrix(3,4,1,-1,1,1,0,1,1,-2,0,0,-1,0))}}}


Multiply Row 3 by {{{-1}}} to make the pivot 1:


{{{(matrix(3,4,1,-1,1,1,0,1,1,-2,0,0,1,0))}}}



Add  -1*Row 3 to Row 2 to get the new Row 2


{{{(matrix(3,4,1,-1,1,1,0,1,0,-2,0,0,1,0))}}}



Add  -1*Row 3 to Row 1 to get the new Row 1


{{{(matrix(3,4,1,-1,0,1,0,1,0,-2,0,0,1,0))}}}



Add  1*Row 2 to Row 1 to get the new Row 1


{{{(matrix(3,4,1,0,0,-1,0,1,0,-2,0,0,1,0))}}}



The matrix is now in <font size=4><b>reduced row echelon form</b></font>


If you need more help with row reduction, check out the <a href="http://www.math.odu.edu/~bogacki/lat/">Linear Algebra Toolkit</a>



Since the right hand column is {{{(matrix(3,1,-1,-2,0))}}} this means that the solutions are {{{x=-1}}}, {{{y=-2}}} and {{{z=0}}}