Set 1: Systems of Equations (Advanced)

Choice C is correct. Choice C is the correct answer. Step 1: Multiply the first equation by 2: 2(5 x - y) = 2(10)$10x - 2 y = 20$$$ Step 2: Compare with the second equation: - Our result: 10x - 2 y = 20$- Given second equation:$10x - 2 y = 15$The left sides are identical, but the right sides are different ($20\neq 15$$). This means the lines are parallel but never intersect. Conclusion: No solution Strategic Tip: When left sides match but right sides don't, the lines are parallel with no intersection. Choice A is incorrect because exactly one solution requires different slopes. Choice B is incorrect because infinitely many solutions requires both sides to match completely. Choice D is incorrect because two linear equations cannot have exactly two solutions.