Question 63463
2x-y-z=-3
x-2y+3z=6
x+y+z=6


(R1)  2 -1 -1  = -3
(R2)  1 -2  3  =  6
(R3)  1  1  1  =  6


R1 + R3 ---->R1


(R1)  3  0  0  =  3
(R2)  1 -2  3  =  6
(R3)  1  1  1  =  6



R2 - R3---->R2


(R1)  3  0  0  =  3
(R2)  0 -3  2  =  0
(R3)  1  1  1  =  6


3R3------>R3


(R1)  3  0  0  =  3
(R2)  0 -3  2  =  0
(R3)  3  3  3  = 18


R3 - R1 ------>R3


(R1)  3  0  0  =  3
(R2)  0 -3  2  =  0
(R3)  0  3  3  = 15


R3 + R2 ------->R3


(R1)  3  0  0  =  3
(R2)  0 -3  2  =  0
(R3)  0  0  5  = 15


5R2---->R2 and 2R3----->R3


(R1)  3  0  0  =   3
(R2)  0 -15 10  =  0
(R3)  0  0  10  =  30


R2-R3----R2


(R1)  3  0  0  =   3
(R2)  0 -15 0  =  -30
(R3)  0  0  10  =  30


(R1)/3---->R1;  (R2)/-15---->R2;  (R3)/10---->R3


(R1)  1  0  0  =   1
(R2)  0  1  0  =   2
(R3)  0  0  1  =   3

x=1
y=2
z=3

Hope this helps.  Have a nice holiday season---ptaylor