Answer
See graph 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. $x - y \gt 0$
$-y \gt -x$
$y \lt x$
Graph $y^2 = 4 - x^2$ and $y = x$ with a solid and dashed line, respectively.
Equation 1 and 2 are $\leq or \lt$, so the shading will be inside and below the graph, respectively.
The solution set is where the black and green areas overlap.
See graph below.
This solution set is bounded.
