Answer
inconsistent.
Work Step by Step
1. Multiply the 1st equation by 3 and add to the 2nd to get $-11y+4z=40$
2. Multiply the 1st equation by 7 and add to the 3rd to get $-33y+12z=105$ or $-11y+4z=35$
3. Take the difference of the above two equations to get $0=5$, thus the system is inconsistent.