Solve the system \(x+y+z=6\), \(x-y=0\), and \(z=2\).

Solve the system \(x+2y=5\), \(y-z=1\), and \(x+z=4\).

Decide whether the system \(x+y+z=1\), \(2x+2y+2z=3\), and \(x-y=0\) is consistent.

Solve the system \(x+y+z=3\), \(2x-y+z=4\), and \(x+2y-z=0\).