Choice D is the correct answer. For no solution, the system must represent parallel lines (same coefficients on $x$ and $y$, but different constants).

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

• First equation: $3x - 2y = 7$
• Second equation: $6x - 4y = k$

Step 2: If we multiply the first equation by 2: $2(3x - 2y) = 2(7)$$6x - 4y = 14$

Step 3: For the lines to be parallel but not identical:

• If $k = 14$: the lines are identical → infinitely many solutions
• If $k \ eq 14$: the lines are parallel → no solution

💡 Strategic Tip: Parallel lines occur when left sides are proportional but right sides are not.

Choice A is incorrect because$k = 7$ gives no solution (not 14), but it's not the only value.

Choice B is incorrect because$k = 10$ gives no solution, but it's not the only value.

Choice C is incorrect because$k = 14$ gives infinitely many solutions, not no solution.