Final answer:
The system of inequalities with no solution is A. y < 2x - 4 and y > 2x + 1.
Step-by-step explanation:
To determine which system of inequalities has no solution, we need to analyze each option and identify any inconsistencies or contradictions.
A. The system of inequalities y < 2x - 4 and y > 2x + 1 can be graphed as two parallel lines with different slopes. Since these lines will never intersect, this system has no solution.
B. The system of inequalities 2x + y ≥ 3 and y^2 - 2x - 3 can also be graphed. However, the graph of y^2 - 2x - 3 is a quadratic curve, while the graph of 2x + y ≥ 3 is a line. These two graphs will not intersect, so this system has no solution as well.
C. The system of inequalities 4x + 4y < 16 and x > y + 16 can be graphed as two lines. These lines will intersect, meaning there is a solution for this system.
D. The system of inequalities y < -6x - 24 and y < 6x + 6 also has lines that are parallel. Since these lines will never intersect, this system has no solution as well.
Therefore, the correct answer is option A: y < 2x - 4 and y > 2x + 1.