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

Analysis:

• First line: slope = 4, y-intercept = -3
• Second line: slope = $k$, y-intercept = 5

Condition for parallel lines (no solution):

• Same slope: $k = 4$
• Different y-intercepts: $-3 \ eq 5$ ✓ (already different)

With $k = 4$, the lines are parallel and never intersect.

💡 Strategic Tip: In slope-intercept form, equal slopes with different intercepts = no solution.

Choice A is incorrect because $k = -3$ means different slopes (4 and -3), giving one solution.

Choice B is incorrect because $k = 5$ means different slopes, giving one solution.

Choice D is incorrect because $k = -4$ means different slopes, giving one solution.