Set 9: Systems of Equations (Intermediate)

Choice C is correct. Choice C is the correct answer. Step 1: Divide the first equation by 3: $\frac{3 x + 6 y}{3} = \frac{9}{3}x + 2 y = 3$ Step 2: For the system to have: - Infinitely many solutions (same line): $p = 3$ - No solution (parallel): $p \neq 3$ 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.