Set 10: Systems of Equations (Advanced)

Choice C is correct. Choice C is the correct answer. Step 1: Divide the first equation by 5: $\frac{5 x - 10 y}{5} = \frac{15}{5}x - 2 y = 3$ This is exactly the second equation! Conclusion: The lines are identical (coincident), meaning infinitely many solutions. Strategic Tip: Identical lines are a special case—they have infinitely many solutions because every point on one line is also on the other. Choice A is incorrect because no solution requires parallel lines with different constants. Choice B is incorrect because one solution requires different slopes. Choice D is incorrect because both lines have the same slope ($\frac{1}{2}$), not perpendicular slopes.