Difficulty: Easy
Correct Answer: 4
Explanation:
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:
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:
Multiply the first equation by 3: 6x + 9y = 54.Multiply the second equation by 2: 6x + 4y = 34.Subtract: (6x + 9y) − (6x + 4y) = 54 − 34 → 5y = 20 → y = 4.Substitute into 2x + 3y = 18: 2x + 12 = 18 → 2x = 6 → x = 3.Thus the larger number is 4.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
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