Final answer:
To graph the solution set of the system of inequalities, we first need to graph each inequality on the coordinate plane. The solution set is the overlapping area of all the shaded regions. The coordinates of the vertices are (0, 0), (0, 6), and (8, 4).
Step-by-step explanation:
To graph the solution set of the system of inequalities, we first need to graph each inequality on the coordinate plane. Let's start with the inequality x ≥ 0. This inequality represents all the points to the right of the y-axis (including the y-axis itself). So, we shade the area to the right of the y-axis, or the positive x-axis.
Next, we graph the inequality y ≥ 0. This inequality represents all the points above the x-axis (including the x-axis itself). So, we shade the area above the x-axis, or the positive y-axis.
Now, let's graph the inequality x + 2y ≤ 12. To do this, we rewrite the inequality as y ≤ -1/2x + 6 and graph the line y = -1/2x + 6. This line has a slope of -1/2 and a y-intercept of 6. We can start at the y-intercept (0, 6) and use the slope to find other points. Since it's less than or equal to, we shade the area below the line.
Finally, we graph the inequality y ≤ x + 4. We rewrite it as y ≤ x - 4 and graph the line y = x - 4. This line has a slope of 1 and a y-intercept of -4. We can start at the y-intercept (0, -4) and use the slope to find other points. Again, since it's less than or equal to, we shade the area below the line.
The solution set is the overlapping area of all the shaded regions. To find the vertices, we look for the points where the lines intersect. The coordinates of the vertices are (0, 0), (0, 6), and (8, 4). Since the solution set is bounded by the lines and doesn't extend indefinitely, it is a bounded solution set.