Answer
Please see the graph.
Work Step by Step
Orange line: $y>x^{2}$
Red line: $x+y\ge3$
The red line will be solid (since we have a greater than or equal to sign), while the orange line will be dotted (since it has a greater than sign).
We pick $(1,3)$ to determine what sides of the lines to shade.
$y>x^{2}$
$3>1^{2}$
$3 > 1$ (true, so we shade the side of the line with the point)
$x+y\ge3$
$1+3\ge3$
$4 \ge 3$ (true, so we shade the side of the line with the point)
The overlap of the two graphs is the solution set of the inequalities.
