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