Substituting $\displaystyle{\left({2},-{2}\right)}\usepackage{cmbright}\Huge\$ into $\displaystyle{6}{x}+{3}{y}>{15}\usepackage{cmbright}\Huge\$ gives you $\displaystyle{12}-{6}>{15}\usepackage{cmbright}\Huge\$ , which is a false statement. So $\displaystyle{\left({2},-{2}\right)}\usepackage{cmbright}\Huge\$ is not a solution to the inequality.