Set 3: Systems of Equations (Advanced)

Choice B is correct. Choice B is the correct answer. Step 1: Multiply the first equation by 2: 2(2 x + y) = 2(4)$4x + 2 y = 8$$$ Step 2: Compare with the second equation: - Our result: 4x + 2 y = 8$- Given second equation:$4x + 2 y = 7$The left sides are identical ($4x + 2 y$), but the right sides are different ($8\neq 7$$). Conclusion: The lines are parallel but don't overlap → no solution Strategic Tip: An impossible equation like "8 = 7" signals parallel lines with no intersection. Choice A is incorrect because one solution requires different slopes. Choice C is incorrect because infinitely many solutions requires both sides to match completely. Choice D is incorrect because perpendicular lines have slopes whose product is $-1$. Here both lines have slope $-2$, not perpendicular.