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

Step 1: Notice the first equation's coefficients are 3 times the second's: $9x - 12y = 3(3x - 4y)$

Step 2: Divide the first equation by 3: $\frac{9x - 12y}{3} = \frac{15}{3}$$3x - 4y = 5$

Verification: With $k = 5$: $3(3x - 4y) = 3(5) = 15$$9x - 12y = 15$ ✓

💡 Strategic Tip: When coefficients are scaled by factor 3, the constant must also be scaled by 3.

Choice A is incorrect because $k = 3$ would give parallel lines (no solution).

Choice B is incorrect because $k = 9$ would give parallel lines.

Choice D is incorrect because $k = 15$ would give parallel lines.