Set 2: Systems of Equations (Advanced)

Choice B is correct. Choice B is the correct answer. For no solution, we need parallel lines. Analysis: - First line: slope = -2, y-intercept = 7 - Second line: slope = $k$, y-intercept = 3 Condition for parallel lines: - Same slope: $k = -2$ - Different y-intercepts: 7 ≠ 3 ✓ (already different) With $k = -2$, both lines have slope $-2$ but different y-intercepts, making them parallel with no intersection. Strategic Tip: For no solution in slope-intercept form, match the slopes but keep different intercepts. Choice A is incorrect because $k = 7$ gives different slopes (-2 and 7), resulting in one solution. Choice C is incorrect because $k = 3$ gives different slopes, resulting in one solution. Choice D is incorrect because $k = 2$ gives different slopes, resulting in one solution.