Call equations A, B, C, D. Only 3 should be needed if equations are all independent.
E: 2A-B: 11y-6z=16
F: B-D: 2y-3z=1
G: E-2F: 7y=14, y=2, substitute for y in F: 4-3z=1, z=1. Substitute for y and z in A to D to find x:
x+16-7=12, x=3;
2x+10-8=8, 2x=6, x=3;
4x+6-9=9, 4x=12, x=3;
2x+6-5=7, 2x=6, x=3.
ANSWER: x=3, y=2, z=1.