Final answer:
None of the given options A, B, C, or D satisfy both inequalities in the system. Therefore, none of these points are within the solution set. There may be a mistake in the question or provided options.
Step-by-step explanation:
The student is asking which point is part of the solution set for the system of inequalities y > 3r - 1 and y < 3 + 5. We need to substitute each point into the inequalities to check which one satisfies both.
Let's evaluate option A) (2,1):
- For the first inequality, y (which is 1) should be greater than 3×2 - 1 (which is 5), but 1 is not greater than 5.
- For the second inequality, y (which is 1) should be less than 3 + 5 (which is 8), and that is true. However, since it does not satisfy the first inequality, it is not part of the solution set.
Now, let's evaluate option B) (1,2):
- For the first inequality, y (which is 2) should be greater than 3×1 - 1 (which is 2), but 2 is not greater than 2.
- For the second inequality, y (which is 2) should be less than 3 + 5 (which is 8), and that is true. However, since it doesn't satisfy the first inequality strictly (it should be >, not ≤), point B is not part of the solution set.
Checking the other options:
- Point C) (-3,4): y is 4; 3×(-3) - 1 disqualifies it immediately.
- Point D) (0,0): y is 0; neither inequality is satisfied.
None of the options A, B, C, or D are part of the solution set. There might be an error in the question or the options provided as none of the points satisfy both inequalities.