Question 1090280
{{{2x-y+3z=0}}}
{{{x+2y-z=5}}}
 {{{ 2y+z=1}}}

Rewrite the system in matrix form:

{{{matrix(3,4,2,-1,3,0,1,2,-1,5,0,2,1,1)}}}


divide the 1 row by 2:


{{{matrix(3,4,1,-1/2,3/2,0,1,2,-1,5,0,2,1,1)}}}



Add (-1 * row1) to row2

{{{matrix(3,4,1, -1/2, 3/2, 0,0,5/2,-5/2,5,0,2,1,1)}}}



Divide row2 by {{{5/2}}}

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



Add (-2 * row2) to row3:

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



Divide row3 by {{{3}}}:

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



Add (1 * row3) to row2:

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



Add ({{{-3/2 }}}* row3) to row1:

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



Add ({{{1/2}}} * row2) to row1:

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



Answer:
{{{x = 2}}}
{{{y= 1}}}
{{{z= -1}}}