Choice C is the correct answer. Let's check the relationship.

Step 1: Divide the first equation by 5: $\frac{5x - 10y}{5} = \frac{15}{5}$$x - 2y = 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.