Choice C is the correct answer. Let's rearrange the first equation to compare.

Step 1: Rearrange $y = 5x + 2$ to standard form: $-5x + y = 2$

Multiply by -2: $10x - 2y = -4$

This is exactly the second equation!

Step 2: Both equations represent the same line → infinitely many solutions

💡 Strategic Tip: Converting between slope-intercept and standard form can reveal identical equations.

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 linear equations cannot have exactly three solutions.