Chapter 8 - Systems of Linear Equations and Problem Solving - 8.4 Systems of Equations in Three Variables - 8.4 Exercise Set - Page 537: 9

$$z=2,\:y=1,\:x=3$$

Solving the system of equations using substitution, we find: $$ \begin{bmatrix}2\left(y+z\right)-3y+2z=7\\ -\left(y+z\right)+2y+z=1\end{bmatrix}\\ -\left(-7+4z+z\right)+2\left(-7+4z\right)+z=1\\ \\ z=2 \\ y=-7+4\cdot \:2\\ x=1+2 \\ z=2,\:y=1,\:x=3$$