Answer
Please see the graph for the solution area.
Work Step by Step
Red line: $-x+y<3$
Green line: $y<1$
Purple line: $2x+y>-2$
Red line:
To determine what side of the line to shade, we use a point not on the line. We can use $(0,0)$ for the red line.
$-x+y<3$
$-0+0<3$
$0<3$ is true, so we shade the right side of the line.
Green line:
To determine what side of the line to shade, we use a point not on the line. We can use $(0,0)$ for the green line.
$y<1$
$0<1$ is true, so we shade below the line.
Purple line:
To determine what side of the line to shade, we use a point not on the line. We can use $(0,0)$ for the purple line.
$2x+y>-2$
$2*0+0>-2$
$0+0>-2$
$0>-2$ is true, so we shade the right side of the line.
The solution area is shaded by all three colors.
