Question 1002470
3x+y+z=1
6x+3y-2z=23
-x-5y-4z=-9
<pre>
{{{system(matrix(3,7,

3x,""+"",y,""+"",z,""="",1,
6x,""+"",3y,""-"",2z,""="",23,
-x,""-"",5y,""-"",4z,""="",-9))}}}

Eliminate x from the 2nd equation by 
multiplying the 1st equation by -2 and
then adding it to the 2nd equation: 

{{{system(matrix(4,7,

-6x,""-"",2y,""-"",2z,""="",-2,
6x,""+"",3y,""-"",2z,""="",23,
"--","--","--","--","--","--","--",
"","",y,""-"",4z,""="",21))}}}

{{{system(matrix(3,7,
3x,""+"",y,""+"",z,""="",1,
"","",y,""-"",4z,""="",21,
-x,""-"",5y,""-"",4z,""="",-9))}}}

Eliminate x from the 3rd equation by 
multiplying the 3rd equation by 3 and
then adding the 1st equation to it:

{{{system(matrix(4,7,

-3x,""-"",15y,""-"",12z,""="",-27,
3x,""+"",y,""+"",z,""="",1,
"--","--","--","--","--","--","--",
"","",-14y,""-"",11z,""="",-26))}}}

{{{system(matrix(3,7,
3x,""+"",y,""+"",z,""="",1,
"","",y,""-"",4z,""="",21,
"","",-14y,""-"",11z,""="",-26))}}}

Eliminate y from the 3rd equation by 
multiplying the 2nd equation by 14 and
then adding it to the 3rd equation:

{{{system(matrix(4,5,

14y,""-"",56z,""="",294,
-14y,""-"",11z,""="",-26,
"--","--","--","--","--",
"","",67z,""="",268))}}}

{{{system(matrix(3,7,
3x,""+"",y,""+"",z,""="",1,
"","",y,""-"",4z,""="",21,
"","","","",-67z,""="",268))}}}

Solve the 3rd equation for z

{{{-67z}}}{{{""=""}}}{{{268}}}
{{{z}}}{{{""=""}}}{{{-4}}}

Substitute z=-4 into the 2nd equation

{{{y-4z}}}{{{""=""}}}{{{21}}}
{{{y-4(-4)}}}{{{""=""}}}{{{21}}}
{{{y+16}}}{{{""=""}}}{{{21}}}
{{{y}}}{{{""=""}}}{{{5}}}

Substitute y=5 and z=-4 in the 1st equation

{{{3x+y+z}}}{{{""=""}}}{{{1}}}
{{{3x+(5)+(-4)}}}{{{""=""}}}{{{1}}}
{{{3x+1}}}{{{""=""}}}{{{1}}}
{{{3x}}}{{{""=""}}}{{{0}}}
{{{x}}}{{{""=""}}}{{{0}}}

Solution:  (x,y,z) = (0,5,-4)

Edwin</pre>