Multiply the first equation by 3: $\displaystyle{6}{x}+{9}{y}-{3}{z}={36}\usepackage{cmbright}\Huge\$

Add this to the second equation to get: $\displaystyle{5}{y}-{6}{z}={8}\usepackage{cmbright}\Huge\$

Multiply the third equation by 2: $\displaystyle{6}{x}-{6}{y}+{10}{z}={2}\usepackage{cmbright}\Huge\$

Add this to the second equation to get: $\displaystyle-{10}{y}+{7}{z}=-{26}\usepackage{cmbright}\Huge\$

Multiply the first new equation by 2: $\displaystyle{10}{y}-{12}{z}={16}\usepackage{cmbright}\Huge\$

Add this to the preceding equation to get: $\displaystyle-{5}{z}=-{10}\usepackage{cmbright}\Huge\$ , so $\displaystyle{z}={2}\usepackage{cmbright}\Huge\$

From the preceding equation: $\displaystyle{y}={4}\usepackage{cmbright}\Huge\$

From an original equation: $\displaystyle{x}={1}\usepackage{cmbright}\Huge\$