how to solve gauss jordan reduction using three equations?

Question

2x-3y+x=2

x+y+z=8

3x-y-z+0

Answer 1

Augmented matrix format:

( 2 -3 1 | 2 )

( 1 1 1 | 8 )

( 3 -1 -1 | 0 )

R1⇔R2:

( 1 1 1 | 8 )

( 2 -3 1 | 2 )

( 3 -1 -1 | 0 )

R2-2R1 then R2*-1:

( 1 1 1 | 8 )

( 0 5 1 | 14 )

( 3 -1 -1 | 0 )

R3-3R1 then R3*(-1/4):

( 1 1 1 | 8 )

( 0 5 1 | 14 )

( 0 1 1 | 6 )

R2-R3 then R2/4:

( 1 1 1 | 8 )

( 0 1 0 | 2 )

( 0 1 1 | 6 )

R1-R3:

( 1 0 0 | 2 )

( 0 1 0 | 2 )

( 0 1 1 | 6 )

R3-R2:

( 1 0 0 | 2 )

( 0 1 0 | 2 )

( 0 0 1 | 4 )

(x,y,z)=(2,2,4)