Set 13: Systems of Equations (Advanced)

Choice C is correct. 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: $-3 \neq 5$ ✓ (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.