Compare x and y (determine a single relation): I. x^2 − 11x + 24 = 0 II. 2y^2 − 9y + 9 = 0 Choose the correct relationship between x and y: x > y, x < y, x = y, or cannot be determined.

Introduction / Context:
Both equations yield two real roots. We must determine if a single relation holds for all valid pairings or if the relation varies by choice.

Given Data / Assumptions:

• I: x^2 − 11x + 24 = 0 ⇒ (x − 3)(x − 8) = 0 ⇒ x ∈ {3, 8}.
• II: 2y^2 − 9y + 9 = 0.

Concept / Approach:
Find y-roots and compare the sets. Overlap or crossing indicates indeterminacy.

Step-by-Step Solution:

Verification / Alternative check:
Construct a small table of pairings to confirm that x is never less than y but sometimes equal and sometimes greater. Because options usually demand a unique statement, we choose “Relationship cannot be determined.”

Why Other Options Are Wrong:

• x < y: Never occurs.
• x = y: Occurs only for one pairing (3, 3).
• x > y: Not universal since equality is also possible.

Common Pitfalls:
Ignoring that equality at 3 occurs, which prevents a strict x > y conclusion.

Final Answer: