What is the value of x + y in the solution of the equations (x/4) + (y/3) =…

Concept: To solve a system of two linear equations in two variables, first clear any fractions to write both equations in standard integer form (ax + by = c), then eliminate one variable by combining the equations so only one unknown remains.

Applying this to the given equations:

1. Multiply (x/4) + (y/3) = 5/12 by 12 (the LCM of 4, 3, and 12) to clear denominators: 3x + 4y = 5 ... (i)

2. Multiply (x/2) + y = 1 by 2 (the LCM of 2 and 1) to clear denominators: x + 2y = 2 ... (ii)

3. Subtract equation (ii) from equation (i): (3x + 4y) - (x + 2y) = 5 - 2, which gives 2x + 2y = 3.

4. Divide both sides by 2: x + y = 3/2.

Cross-check: Solving (ii) for x gives x = 2 - 2y. Substituting into (i): 3(2 - 2y) + 4y = 5, so 6 - 2y = 5, giving y = 1/2 and x = 1. Both values satisfy the original equations: (1/4) + (1/6) = 5/12 and (1/2) + (1/2) = 1, confirming x + y = 3/2.