Only the rows that change will be shown in the following solution.
Initial matrix:
( 1 1 1 | 6 )
( 3 3 4 | 20 )
( 2 1 3 | 13 )
R2-R3: ( 1 2 1 | 7 ); R2-R1: ( 0 1 0 | 1 ); R1-R2: ( 1 0 1 | 5 ); R3-2R1: ( 0 1 1 | 3 );
R3-R2: ( 0 0 1 | 2 ); R1-R3: ( 1 0 0 | 3).
x=3; y=1; z=2. Check:
( 3 1 2 | 6 )
( 9 3 8 | 20 )
( 6 1 6 | 13 )