Correct. Add the first and third equations: $\displaystyle-{x}+{10}{z}={6}\usepackage{cmbright}\Huge\$

Add the second and third equations: $\displaystyle{x}+{8}{z}={12}\usepackage{cmbright}\Huge\$

Add these two new equations: $\displaystyle{18}{z}={18}\usepackage{cmbright}\Huge\$ , so $\displaystyle{z}={1}\usepackage{cmbright}\Huge\$

Substitute into the first new equation: $\displaystyle-{x}+{10}={6}\usepackage{cmbright}\Huge\$ , so $\displaystyle{x}={4}\usepackage{cmbright}\Huge\$

Substitute x and z into the third equation: $\displaystyle{12}+{y}+{4}={14}\usepackage{cmbright}\Huge\$ , so $\displaystyle{y}=-{2}\usepackage{cmbright}\Huge\$