Set 3: Systems of Equations (Advanced)

Choice C is correct. Choice C is the correct answer. For infinitely many solutions, one equation must be a multiple of the other. Step 1: Notice that the first equation's coefficients are double the second's: $6x + 8 y = 2(3 x + 4 y)$ Step 2: Divide the first equation by 2: \frac{6 x + 8 y}{2} = \frac{24}{2}$3x + 4 y = 12$$$ Verification: With $c = 12$, the first equation is exactly double the second: 2(3 x + 4 y) = 2(12) = 24$$ ✓ Strategic Tip: Scaling coefficients by a factor requires scaling the constant by the same factor. Choice A is incorrect because $c = 6$ would give parallel lines (no solution). Choice B is incorrect because $c = 8$ would give parallel lines. Choice D is incorrect because $c = 24$ would give parallel lines.