Answer
Please see the graph.
Work Step by Step
Blue line: $y\ge x+1$
Orange line: $y\ge3-x$
To determine what sides of the lines to shade, we use a point not on the line. We can use $(0,0)$ for both lines.
Blue line:
$y\ge x+1$
$0\ge 0+1$
$0 \ge 1$ (false, so we shade the left side of the line)
Orange line:
$y \ge 3-x$
$0 \ge 3-0$
$0 \ge 3$ (false, so we shade the right side of the line)
The solution area is the area where both inequalities overlap.
