Answer
See below.
Work Step by Step
The question asks to graph the solution set of the system of inequalities.
Here are some criteria for graphing inequalities:
1. If it is $\lt$ or $\gt$, then the graph must be dashed.
2. If it is $\leq$ or $ \geq$, then the graph must be solid.
3. If it is $\lt$ or $\leq$ (with y being isolated), then the shading is below, left, or inside the graph.
4. If it is $\gt$ or $\geq$ (with y being isolated), then the shading is above, right, or outside the graph.
Given:
1. $x^2 + y^2 \leq 4$
$y^2 \leq 4 - x^2$
2. $x^2 - 2y \gt 1$
$-2y \gt 1 - x^2$
$y \lt 1/2x^2 - 1/2$
Graph $y^2 = 4 - x^2$ and $y =1/2x^2 - 1/2$ with a solid and dashed line, respectively.
Equation 1 and 2 is $\leq or \lt $, so the shading will be inside or below the graph.
The solution set is where the black and green areas overlap.
See graph below.
This solution set is not bounded.
