Choice C is the correct answer. For no solution, we need parallel lines.

Step 1: Notice the second equation's coefficients are double the first's: $8x + 10y = 2(4x + 5y)$

Step 2: Multiply the first equation by 2: $2(4x + 5y) = 2(12) = 24$$8x + 10y = 24$

Analysis:

• If $b = 24$: equations are identical → infinitely many solutions
• If $b \ eq 24$: parallel lines → no solution

Conclusion: Any value except 24 gives no solution.

💡 Strategic Tip: When left sides are proportional, the constant determines whether lines are identical or parallel.

Choice A is incorrect because $b = 24$ gives infinitely many solutions, not no solution.

Choice B is incorrect because while $b = 12$ gives no solution, it's not the only value.

Choice D is incorrect because while $b = 6$ gives no solution, it's not the only value.