There are two numbers x and y such that 2x + 3y = 18 and 3x + 2y = 17. What is the larger of the two numbers?

Introduction / Context:
This is a linear system in two variables. Solving simultaneously (by elimination or substitution) yields the unique pair. The final request is to select the larger of x and y from the solution pair.

Given Data / Assumptions:

• 2x + 3y = 18.
• 3x + 2y = 17.
• We seek max{x, y}.

Concept / Approach:
Use elimination: align coefficients of one variable and subtract equations to isolate the other variable. After finding y, back-substitute to compute x. Compare the two values to determine the larger.

Step-by-Step Solution:

Verification / Alternative check:
Check in the second equation: 3x + 2y = 9 + 8 = 17, correct. Consistency confirms the solution.

Why Other Options Are Wrong:
6, 8, and 12 are not values of x or y here. 5 is not obtained from the system. The correct larger value among (3, 4) is 4.

Common Pitfalls:
Arithmetic slips during elimination, or mixing which equation to multiply—both can create sign errors and wrong results.

Final Answer:
4