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. $x + y \lt 10$
$y \lt 10 - x$
2. $x^2 + y^2 \gt 9$
$y^2 \gt 9 - x^2$
Graph $y =10 - x$ and $y^2 = 9 - x^2$ with a dashed line and a domain restriction of $x \gt 0, y \gt 0$ .
Equation 1 is $\lt$, so the shading will be below the graph,
Equation 2 is $\gt$, so the shading will be outside the graph,
The solution set is where the black and green areas overlap.
See graph below.
This solution set is not bounded.
