Question 30595
3X-2Y+8Z=9
-2X+2Y+z=3
X+2y-3Z=8 
Writing it out in augmented matrix form, (1), (2) and (3)refer to the 1st, 2nd and 3rd eqns at each step.
I hope you can follow this. The row operations are in between each step.
 3 -2  8|9
-2  2  1|3
 1  2 -3|8
(1)- 3*(3), (2) + 2*(3)
0 -8 17|-15
0 6 -5|19
1 2 -3|8
3*(1), 3*(3),
0 -24 51|-45
0 6 -5|19
3 6 -9|24
(1) + 4*(2), (3) - (2),
0 0 31|31
0 6 -5|19
3 0 -4|5
(1)/31,
0 0 1|1
0 6 -5|19
3 0 -4|5
(2) + 5*(1), (3) + 4*(1)
0 0 1|1
0 6 0|24
3 0 0|9
(2)/6, (3)/3,
0 0 1|1
0 1 0|4
1 0 0|3
Hence:x = 3, y = 4, z = 1
=========================