Correct. Add the first and second equations: $\displaystyle{3}{x}+{5}{y}={21}\usepackage{cmbright}\Huge\$

Add the first and third equations: $\displaystyle-{3}{x}+{2}{y}={21}\usepackage{cmbright}\Huge\$

Add these two new equations: $\displaystyle{7}{y}={42}\usepackage{cmbright}\Huge\$ , so $\displaystyle{y}={6}\usepackage{cmbright}\Huge\$

Substitute into the first new equation: $\displaystyle{3}{x}+{30}={21}\usepackage{cmbright}\Huge\$ , so $\displaystyle{x}=-{3}\usepackage{cmbright}\Huge\$

Substitute x and y into the second equation: $\displaystyle-{3}+{12}+{z}={11}\usepackage{cmbright}\Huge\$ , so $\displaystyle{z}={2}\usepackage{cmbright}\Huge\$