Set 13: Systems of Equations (Advanced)

Choice C is correct. Choice C is the correct answer. Step 1: Multiply the first equation by 2: 2(3 x + y) = 2(12)$6x + 2 y = 24$$$ Step 2: Compare with the second equation: - Our result: 6x + 2 y = 24$- Given:$6x + 2 y = 20$This gives us$24= 20$$, 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.