Choice C is the correct answer. Let's check if the second equation is a multiple of the first.

Step 1: Multiply the first equation by 2: $2(5x - y) = 2(10)$$10x - 2y = 20$

Step 2: Compare with the second equation:

• Our result: $10x - 2y = 20$
• Given second equation: $10x - 2y = 15$

The left sides are identical, but the right sides are different ($20 \ eq 15$). 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.