Choice B is the correct answer. Let's analyze each system:

System I: $y = 2x + 5$ and $y = 2x - 3$

• Same slope (2), different intercepts
• Parallel lines ✓

System II: $y = 2x + 5$ and $y = -\frac{1}{2}x + 5$

• Different slopes (2 and $-\frac{1}{2}$)
• 💡 Strategic Tip:
• Parallel: same slope, different intercepts
• Perpendicular: slopes multiply to -1
• Identical: same slope, same intercept

Choice A is incorrect because System II has perpendicular lines, not parallel.

Choice C is incorrect because System III has identical lines, and System II is perpendicular.

Choice D is incorrect because System III has identical lines, not parallel (though all identical lines are technically parallel, "parallel" usually means "distinct parallel lines").