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: $4x + 2y = 8$
• Second: $2x + y = k$

Step 2: Divide the first equation by 2: $\frac{4x + 2y}{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).