Final answer:
To find points in the solution set of the system of inequalities, we can solve each inequality separately. For the inequality -3x - y < 12, one possible point is (0, -11). For the inequality 2x + 3y ≥ 9, two possible points are (0, 3) and (4.5, 0).
Step-by-step explanation:
To find points that are members of the solution set, we can solve the system of inequalities. Let's start with the first inequality, -3x - y < 12:
1. Pick a value for x. For example, let x = 0.
2. Substitute the value of x into the inequality:
-3(0) - y < 12
-y < 12
y > -12
So when x = 0, y can be any value greater than -12. One possible point is (0, -11).
3. Repeat steps 1 and 2 to find two more points that are members of the solution set.
For the second inequality, 2x + 3y ≥ 9:
1. Let x = 0:
2(0) + 3y ≥ 9
3y ≥ 9
y ≥ 3
So when x = 0, y can be any value greater than or equal to 3. Another possible point is (0, 3).
2. Let y = 0:
2x + 3(0) ≥ 9
2x ≥ 9
x ≥ 4.5
So when y = 0, x can be any value greater than or equal to 4.5. One more possible point is (4.5, 0).