Compare x and y (define the answer codes): I. 4x + 7y = 209 II. 12x − 14y = −38 Choose one option: A) x > y B) x < y C) x = y D) Relationship cannot be determined

Introduction / Context:
We are given two linear equations in x and y and asked to compare their values. The most reliable approach is to solve the system exactly and then compare the numerical values. The answer codes are provided explicitly to avoid ambiguity common in comparison problems.

Given Data / Assumptions:

• I: 4x + 7y = 209
• II: 12x − 14y = −38
• Real numbers x, y.

Concept / Approach:
Use elimination or substitution to solve the simultaneous linear equations. Then compare the found x and y to select the appropriate code (A, B, C, or D).

Step-by-Step Solution:

Verification / Alternative check:
Check in II: 12*19 − 14*19 = (12 − 14)*19 = −2*19 = −38, which matches II exactly.

Why Other Options Are Wrong:

• x > y or x < y: Both false since x and y are equal.
• Relationship cannot be determined: The system gives a unique solution, so the relationship is determined.

Common Pitfalls:
Arithmetic slips during elimination (especially sign errors when subtracting). Always verify by substituting the result into both equations.

Final Answer: