Substitute $\displaystyle{x}=-{8}\usepackage{cmbright}\Huge\$ and $\displaystyle{y}={2}\usepackage{cmbright}\Huge\$ into each inequality and simplify:

$\displaystyle-{8}-{2}{\left({2}\right)}<{4}\usepackage{cmbright}\Huge\$ or $\displaystyle-{12}<{4}\usepackage{cmbright}\Huge\$ TRUE

$\displaystyle{2}>-{2}{\left(-{8}\right)}-{5}\usepackage{cmbright}\Huge\$ or $\displaystyle{2}>{11}\usepackage{cmbright}\Huge\$ FALSE

For an ordered pair to be a solution of a system it must be a solution of both inequalities.