The graph of this system of inequalities is shown below. The boundary lines are dashed because both inequalities are $\displaystyle>\usepackage{cmbright}\Huge\$ . The solution to $\displaystyle{x}+{y}>{1}\usepackage{cmbright}\Huge\$ is shown in orange. The solution to $\displaystyle{x}-{y}>{1}\usepackage{cmbright}\Huge\$ is shown in blue. The overlapping region in purple is partly in Quadrant I and partly in Quadrant IV.