Choice C is the correct answer. For infinitely many solutions, the second equation must be a multiple of the first.

Step 1: Notice that $9x + 12y$ is exactly $3(3x + 4y)$.

Step 2: For the equations to be equivalent: $9x + 12y = 3(3x + 4y) = 3(12) = 36$

Verification:

• First equation: $3x + 4y = 12$
• Second equation (with $b = 36$): $9x + 12y = 36$
• Divide second by 3: $3x + 4y = 12$ ✓ (same as first)

💡 Strategic Tip: If coefficients are scaled by a factor, the constant must be scaled by the same factor for infinite solutions.

Choice A is incorrect because $b = 24$ would give no solution (parallel lines).

Choice B is incorrect because $b = 12$ would give no solution.

Choice D is incorrect because $b = 48$ would give no solution.