Set 9: Systems of Equations

Choice C is correct. 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: $5x - 2 y = 10$ - Second: $10x - 4 y = a$ Step 2: Multiply the first equation by 2: $$2(5 x - 2 y) = 2(10)10x - 4 y = 20$$$ 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.