Set 2: Linear Inequalities (Intermediate)

Explanation

Answer: A

Which statement is true about the system $y > 2x$ and $y < 2x - 4$ ?

It has no solution.

✓ Correct

The solution is a strip between lines.

The solution is the entire plane.

It has exactly one solution.

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Analyze geometry. 1. Lines: Parallel ( $m=2$ ). 2. Regions: Above the top line ( $y > 2 x$ ) vs Below the bottom line ( $y < 2 x - 4$ ). Note: $2x > 2 x-4$ , so $y=2 x$ is above $y=2 x-4$ . 3. Overlap: None. Strategic Tip: Sketching quickly reveals disjoint regions. Choice B is incorrect because that would be $2x-4 < y < 2 x$ . Choice C is incorrect. Choice D is incorrect.

Key Steps:

•

The correct answer is It has no solution.

Why others are wrong:

B: Choice B is incorrect and may result from a calculation error.

C: Choice C is incorrect and may result from a calculation error.

D: Choice D is incorrect and may result from a calculation error.

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