Multiply the first equation by 2: $\displaystyle{8}{x}-{4}{y}-{10}{z}=-{18}\usepackage{cmbright}\Huge\$

Add this to the second equation to get: $\displaystyle{3}{x}-{4}{z}=-{6}\usepackage{cmbright}\Huge\$

Multiply the second equation by 2: $\displaystyle-{10}{x}+{8}{y}+{12}{z}={24}\usepackage{cmbright}\Huge\$

Add this to the third equation to get: $\displaystyle-{7}{x}+{4}{z}=-{2}\usepackage{cmbright}\Huge\$

Add this to the preceding equation with x and z to get: $\displaystyle-{4}{x}=-{8}\usepackage{cmbright}\Huge\$ , so $\displaystyle{x}={2}\usepackage{cmbright}\Huge\$

From the preceding equation: $\displaystyle{z}={3}\usepackage{cmbright}\Huge\$

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