Choice C is the correct answer. For infinitely many solutions, the second equation must be a multiple of the first.

Step 1: Notice that the coefficients in the second equation are exactly double those in the first:

• First: $5x - 2y = 10$
• Second: $10x - 4y = a$

Step 2: Multiply the first equation by 2: $2(5x - 2y) = 2(10)$$10x - 4y = 20$

Verification: With $a = 20$, the second equation is exactly double the first, 💡 Strategic Tip: When coefficients are scaled by a factor, the constant must be scaled by the same factor.

Choice A is incorrect because $a = 10$ would give parallel lines (no solution).

Choice B is incorrect because $a = 5$ would give parallel lines.

Choice D is incorrect because $a = 40$ would give parallel lines.