Set 13: Systems of Equations (Advanced)

Choice B is correct. Choice B is the correct answer. System I: $y = 2 x + 5$ and $y = 2 x - 3$ - Same slope (2), different intercepts - Parallel lines ✓ System II: $y = 2 x + 5$ 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").