Add the first and second equations: $\displaystyle{2}{y}+{2}{z}={2}\usepackage{cmbright}\Huge\$

Add the first and third equations: $\displaystyle{3}{y}-{2}{z}={8}\usepackage{cmbright}\Huge\$

Add the two new equations: $\displaystyle{5}{y}={10}\usepackage{cmbright}\Huge\$ , so $\displaystyle{y}={2}\usepackage{cmbright}\Huge\$

Substitute this into the first new equation: $\displaystyle{4}+{2}{z}={2}\usepackage{cmbright}\Huge\$ , so $\displaystyle{z}=-{1}\usepackage{cmbright}\Huge\$

Substitute y and z into the third equation: $\displaystyle{2}{x}-{4}-{1}={3}\usepackage{cmbright}\Huge\$ , so $\displaystyle{x}={4}\usepackage{cmbright}\Huge\$

Check your solution in all three equations.