x+y+z=11, x-y+z=5, x-z=y+1 and solve it by any of the methods: isolation, elimination or determinants. isolation (or back substitution, would be for instance: z = 11-x-y, z=5-x+y, z = x-y-1 and then impose z=z:
11-x-y=5-x+y,
11-x-y=x-y-1,
The first takes you to: 6=2y or y=3, then the second to 12=2x or x=6, so that:
x=6, y=3, z=2.
You can see that it checks out
