Final answer:
The solution to the system of inequalities y > 2x² - 8 and y ≤ x² - 3x + 4 can be found by testing each of the ordered pairs. The only ordered pair that satisfies both inequalities is (0, -5), which corresponds to option D.
Step-by-step explanation:
The student's question relates to finding a solution for a system of inequalities. The given system consists of two inequalities: y > 2x² - 8 and y ≤ x² - 3x + 4. Let's evaluate each of the given ordered pairs to find the correct one.
To evaluate each ordered pair, we will plug the x-coordinate into the inequalities and check if the resulting value is less than or equal to the y-coordinate for the second inequality and greater than for the first.
For (5,0): y should be greater than 2(5)² - 8 = 42 and less than or equal to 5² - 3(5) + 4 = 14. Zero does not satisfy either inequality.
For (-3, -2): y should be greater than 2(-3)² - 8 = 10 and less than or equal to (-3)² - 3(-3) + 4 = 16. Minus two does not satisfy the first inequality.
For (4, -3): y should be greater than 2(4)² - 8 = 24 and less than or equal to 4² - 3(4) + 4 = 8. Minus three does not satisfy the first inequality.
For (0, -5): y should be greater than 2(0)² - 8 = -8 and less than or equal to 0² - 3(0) + 4 = 4. Minus five satisfies both inequalities, making it the correct option.
Therefore, the correct ordered pair that is a solution to the given system of inequalities is (0, -5), which corresponds to option D.