Choice C is the correct answer. Let's find when the lines are parallel but not identical.

Step 1: Divide the first equation by 3: $\frac{3x + 6y}{3} = \frac{9}{3}$$x + 2y = 3$

Step 2: For the system to have:

• Infinitely many solutions (same line): $p = 3$
• No solution (parallel): $p \ eq 3$

💡 Strategic Tip: When left sides are identical after simplification, different right sides = no solution.

Choice A is incorrect because while $p = 9$ gives no solution, it's not the only value.

Choice B is incorrect because while $p = 6$ gives no solution, it's not the only value.

Choice D is incorrect because $p = 3$ gives infinitely many solutions, not no solution.