Answer
$$z=2,\:y=-2,\:x=1$$
Work Step by Step
Solving the system of equations using substitution, we find:
$$ 1+\frac{-4z+2}{3}+z+\frac{-4z+2}{3}+3z=5 \\ z=2 \\ y=\frac{-4\cdot \:2+2}{3}=-2 \\ x=1-2+2=1$$
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