Choice D is the correct answer. For no solution, we need parallel lines (proportional coefficients but different constants).

Step 1: Notice the second equation's coefficients are double the first: $2(2x - 5y) = 2(10) = 20$$4x - 10y = 20$

Step 2: Analysis:

• If $k = 20$: equations are identical → infinitely many solutions
• If $k \ eq 20$: equations have same left side but different right side → parallel lines → no solution

Conclusion: No solution for any value except 20.

💡 Strategic Tip: Parallel lines occur when left sides are proportional but right sides aren't.

Choice A is incorrect because $k = 20$ gives infinitely many solutions, not no solution.

Choice B is incorrect because while $k = 5$ gives no solution, it's not the only such value.

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