Solve the simultaneous linear equations and compare x and y (use mapping below): I. 5x + 2y = 31 II. 3x + 7y = 36 Mapping: 1 → x > y, 2 → x < y, 3 → x = y, 4 → Relationship cannot be determined.

Introduction / Context:
Two linear equations in two variables determine a unique solution pair (x, y). After solving, compare the numeric values directly to choose the correct relation using the provided mapping.

Given Data / Assumptions:

• 5x + 2y = 31
• 3x + 7y = 36
• Coefficients are such that a single unique solution exists.

Concept / Approach:
Use elimination. Align coefficients of y to subtract and solve for x, then back-substitute to find y. Finally, compare x and y numerically.

Step-by-Step Solution:
Multiply the first equation by 7: 35x + 14y = 217Multiply the second by 2: 6x + 14y = 72Subtract: (35x − 6x) + (14y − 14y) = 217 − 72 ⇒ 29x = 145 ⇒ x = 5Back-substitute: 5*5 + 2y = 31 ⇒ 25 + 2y = 31 ⇒ y = 3Comparison: x = 5 and y = 3 ⇒ x > y

Verification / Alternative check:
Plug x = 5, y = 3 into both equations to verify: 25 + 6 = 31 and 15 + 21 = 36. Both hold, confirming the unique pair.

Why Other Options Are Wrong:
“x < y” and “x = y” contradict the computed values; “Relationship cannot be determined” is invalid because the system gives a unique, checkable solution.

Common Pitfalls:
Arithmetic slips when multiplying or subtracting the equations; recheck the elimination step carefully.

Final Answer:
x > y