Choice C is the correct answer. For infinitely many solutions, the equations must be multiples of each other.

Step 1: Notice the first equation's coefficients are 4 times the second's: $8x - 12y = 4(2x - 3y)$

Step 2: Divide the first equation by 4: $\frac{8x - 12y}{4} = \frac{20}{4}$$2x - 3y = 5$

Verification: With $k = 5$, multiply second by 4: $4(2x - 3y) = 4(5) = 20$$8x - 12y = 20$ ✓ (matches first equation)

💡 Strategic Tip: If coefficients are scaled by factor $n$, the constant must also be scaled by $n$.

Choice A is incorrect because $k = 20$ would give parallel lines (no solution).

Choice B is incorrect because $k = 8$ would give parallel lines.

Choice D is incorrect because $k = 10$ would give parallel lines.