Set 10: Systems of Equations (Intermediate)

Choice C is correct. Choice C is the correct answer. For infinitely many solutions, the second equation must be a multiple of the first (or vice versa). Step 1: Notice that the first equation's coefficients are double the second: - First: $4x + 2 y = 8$ - Second: $2x + y = k$ Step 2: Divide the first equation by 2: \frac{4 x + 2 y}{2} = \frac{8}{2}$2x + y = 4$$$ Step 3: For the equations to be identical: k = 4$$ With $k = 4$, both equations represent the same line, giving infinitely many solutions. Strategic Tip: For infinitely many solutions, one equation must be a scalar multiple of the other (including the constant term). Choice A is incorrect because $k = 2$ would make the lines parallel (no solution), not identical. Choice B is incorrect because $k = 8$ would make the lines parallel (no solution). Choice D is incorrect because $k = 6$ would make the lines parallel (no solution).