Answer
Please see the graph.
Work Step by Step
The green line is the graph $x+y\ge1$ and has a solid line since it has a greater than or equal to sign. The blue line is the graph $2x+3y<1$ and has a dotted line since it has a less than sign. The orange line is the graph $x>-3$ and has a dotted line since it has a greater than sign.
We also pick the point $(0,2)$ to determine what sides of the graphs to shade.
$(0,2)$
$x+y\ge1$
$0+2\ge1$
$2 \ge 1$ (true, so we shade the side of the graph with the point)
$(0,2)$
$2x+3y<1$
$2*0+3*2<1$
$0+6 < 1$
$6 < 1$ (false, so we shade the side of the graph without the point)
$(0,2)$
$x>-3$
$0>-3$
$0 > -3$ (true, so we shade the side of the graph with the point)
The overlap of the graphs is the solution set.
