Solve a linear pair to find x: If 3x + y = 81 and 81x − y = 3, determine the value of x.

Introduction / Context:We are given two linear equations in x and y. Adding them immediately eliminates y, giving x directly without the need for substitution or more complex algebra.

Given Data / Assumptions:

• 3x + y = 81
• 81x − y = 3

Concept / Approach:Use elimination by addition: adding the two equations cancels y. Solve for x and then (optionally) back-solve for y to verify.

Step-by-Step Solution:(3x + y) + (81x − y) = 81 + 384x = 84 → x = 1(Optional) y = 81 − 3x = 81 − 3 = 78

Verification / Alternative check:Check the second equation: 81*1 − 78 = 3, which holds.

Why Other Options Are Wrong:17/16, 17/8, 17/4, and 15/4 do not satisfy both equations; only x = 1 does.

Common Pitfalls:Attempting substitution and making arithmetic slips with large coefficients. Elimination here is faster and reduces error risk.

Final Answer:1