#### Answer

$$z=-6,\:y=-5,\:x=2$$

#### Work Step by Step

Solving the system of equations using substitution, we find:
$$ \frac{4-4\left(-\frac{-21z-11}{23}\right)+3z}{3}+2\left(-\frac{-21z-11}{23}\right)-z=-2 \\ z=-6 \\ y=-\frac{-21\left(-6\right)-11}{23}=-5 \\ x=\frac{4-4\left(-5\right)+3\left(-6\right)}{3}=2$$