Final answer:
The correct answer to which function could be added to the given system of inequalities without changing the solution set is B) y < 3. This inequality overlaps with the original solution set, ensuring no solutions are excluded.
Step-by-step explanation:
The question asks us to consider which function could be added to a system of inequalities without changing the solution set. The given system of inequalities is 5x + 2y > 3x - 3. By solving this inequality for y, we get y > (3x - 3 - 5x)/2, which simplifies to y > -x - 1.5. For any function to not change the solution set, it must not conflict with the existing inequality, meaning it would have to be a less restrictive condition (more values for y would satisfy it).
Adding function A) y > 2 would be a stricter constraint on y than the original, potentially excluding values that would otherwise satisfy the initial inequality. Option C) y < 2 is a less restrictive constraint on y, as it allows all values below 2 and the original inequality y > -x - 1.5 also allows values below 2 for some x. However, to ensure that the added inequality does not conflict with the original solution set, we must pick the option that is always true given the original. In this case, it would be Option B) y < 3, because for any pair of (x,y) that satisfies y > -x - 1.5, y is also less than 3; thus, adding y < 3 does not change the solutions set. Options A, C, and D could potentially exclude solutions that the original allows.
Therefore, the correct answer is B) y < 3, as adding this inequality does not change the set of solutions.