Choice C is the correct answer. Let's check the consistency.

Step 1: Multiply the first equation by 2: $2(3x + y) = 2(12)$$6x + 2y = 24$

Step 2: Compare with the second equation:

• Our result: $6x + 2y = 24$
• Given: $6x + 2y = 20$

This gives us $24 = 20$, which is impossible!

Conclusion: The lines are parallel but don't overlap → no solution

💡 Strategic Tip: When simplification leads to a false statement (like 24 = 20), the system has no solution.

Choice A is incorrect because infinite solutions require both sides to match completely.

Choice B is incorrect because one solution requires different slopes.

Choice D is incorrect because both lines have slope $-3$, not perpendicular slopes.