Difficulty: Easy
Correct Answer: 3/2
Explanation:
Introduction: Two linear equations in two variables can be solved by substitution or elimination. After finding x and y, compute x + y. The fractions reduce cleanly, making arithmetic straightforward.
Given Data / Assumptions:
Concept / Approach: Convert the first equation to a common denominator, or express one variable from the second equation and substitute into the first. Solve precisely to avoid rounding.
Step-by-Step Solution:
From (x/2) + y = 1 → y = 1 − x/2.Substitute into (x/4) + (y/3) = 5/12:x/4 + (1 − x/2)/3 = 5/12 → x/4 + 1/3 − x/6 = 5/12.Take common denominator 12: 3x − 2x + 4 = 5 → x = 1.Then y = 1 − 1/2 = 1/2 → x + y = 3/2.Verification / Alternative check: Plug x = 1, y = 1/2 back: LHS of first = 1/4 + 1/6 = 5/12; second = 1/2 + 1/2 = 1. Both satisfy the system.
Why Other Options Are Wrong: 1, 2, 4, and 5/2 do not match the computed sum x + y = 3/2.
Common Pitfalls: Mishandling fractional arithmetic or failing to reduce 10/24 to 5/12 correctly.
Final Answer: 3/2
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