Final answer:
To graph the solution set of the system of inequalities, we need to first graph each individual inequality and then find the intersection of their solution sets. The solution set is bounded and its vertices are (0,0), (3,0), and (0,-3).
Step-by-step explanation:
To graph the solution set of the system of inequalities, we need to first graph each individual inequality and then find the intersection of their solution sets. Let's start with the first inequality:
The inequality x^2 + y^2 < 9 represents a circle with center at the origin (0,0) and radius 3. However, since the inequality is strict (less than), the circle will be open and only the points inside the circle will be included in the solution set.
Now let's graph the second inequality:
The inequality x + y < 0 represents a line with slope -1 passing through the origin. Shade the region below this line to include all the points that satisfy the inequality.
To find the solution set, we need to see where these two shaded regions overlap. The solution set will be the intersection of these shaded regions. In this case, it will be a portion of the circle below the line. The coordinates of the vertices of the solution set are (0,0), (3,0), and (0,-3). The solution set is bounded because it is limited to a region of the graph.