Consider the last set of equations:-
x - y - z = 2...........................(1)
x + y - z = 3..........................(2)
-x + y + z = 4........................(3)
Subtract:- (2) - (1) (x and z's disappear):-
2y = 1
y = 1/2
Now add:- (2) + (3):-
2y = 7
y = 3 1/2
Therefore this set is
inconsistent and independent.
