These equations can be rewritten as $\displaystyle{y}={x}-{4}\usepackage{cmbright}\Huge\$ and $\displaystyle{y}=-{x}-{6}\usepackage{cmbright}\Huge\$ and are shown in the graph, so this is the correct system. However, the solution to the system is the point of intersection, and that point is not $\displaystyle{\left(-{5},-{1}\right)}\usepackage{cmbright}\Huge\$ . Always check your solution back in the original equations. The correct answer is $\displaystyle{y}+{4}={x}\usepackage{cmbright}\Huge\$ and $\displaystyle{x}+{y}=-{6}\usepackage{cmbright}\Huge\$ ; solution $\displaystyle={\left(-{1},-{5}\right)}\usepackage{cmbright}\Huge\$ .