Notice that the left side of the third equation is 2 times the left side of the first equation:
6x - 8y + 2z = 2 (3x - 4y + z)
The first equation says
3x - 4y + z = -5
while the third equation would reduce to
2 (3x - 4y + z) = 10 ⇒ 3x - 4y + z = 5
but -5 ≠ 5, so there is no solution to the system.
