Graph the solution set of the system of linear inequalities below.

You can graph each inequality of the system on the same set of axes.

The graph of $y\le x+1$ is the region on or below the boundary line $y=x+1.$

The graph of $y\ge 1$ is the region on or above the boundary line $y=1.$

Hence, the solution set is the shaded region shown in the following figure: