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.