Solve the system (x/4) + (y/3) = 10/24 and (x/2) + y = 1, and find the value of x + y.

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:

• (x/4) + (y/3) = 10/24 = 5/12.
• (x/2) + y = 1.
• x, y are real numbers.

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:

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