You may have thought this system had an infinite number of solutions because when you attempted to eliminate a variable in the first two equations you got the statement $\displaystyle{0}={0}\usepackage{cmbright}\Huge\$ . However, if you try to eliminate a variable in the second and third equations, you get the statement $\displaystyle{0}={12}\usepackage{cmbright}\Huge\$ . Because this statement is false, this system has no solution.