You may have made an error when attempting to eliminate a variable. A system has no solution only if you end up with an equation such as $\displaystyle{1}={0}\usepackage{cmbright}\Huge\$ . This system has the unique solution $\displaystyle{\left(-{1},{4},{2}\right)}\usepackage{cmbright}\Huge\$ . The correct answer is the system with $\displaystyle{x}+{2}{y}-{3}{z}={4}\usepackage{cmbright}\Huge\$ , $\displaystyle-{x}-{y}+{4}{z}={6}\usepackage{cmbright}\Huge\$ , and $\displaystyle{x}+{6}{y}+{z}={2}\usepackage{cmbright}\Huge\$ .