While solving this system is a form of deductive reasoning, this deduction is incorrect; the deduction must be true for both cases! $\displaystyle{2}+{6}={8}\usepackage{cmbright}\Huge\$ , but $\displaystyle{2}+{1}\ne{12}\usepackage{cmbright}\Huge\$ and $\displaystyle{6}+{1}\ne{4}\usepackage{cmbright}\Huge\$ .