Question 56963
{{{x+2y-z=4}}}
{{{2x-y+3z=8}}}
{{{-2x+3y-2z=10}}}
----------------- add and eliminate z
x + 4y + 0z = 22
:
Mult eq 1 by -2 and add to equation 3
-2x - 4y + 2z = -8
-2x + 3y - 2z = 10
--------------------add
-4x + 1y + 0z = 2
:
Using the two equations with x & y
x  + 4y = 22
-4x + y =  2  mult this equation by 4
:
x  +  4y = 22
-16x + 4y = 8
-----------------
-15x + 0y = 30
       -15x = 30
         x = 30/-15
         x = -2
:
Subsitute -2 for x in x + 4y = 22
-2 + 4y = 22
     4y = 22 + 2
      y = 24/4
y = 6
:
I'll let you find out what z is, check your solutions in one of the original equations.