Set 3: Linear Inequalities (Intermediate)

Explanation

Answer: A

Which system represents the region in Quadrant I bounded by $y = 5$ and $x = 4$ ?

$0 \leq x \leq 4, 0 \leq y \leq 5$

✓ Correct

$x \geq 4, y \geq 5$

$x \leq 4, y \leq 5$

$0 < x < 4, 0 < y < 5$

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Define the rectangular box. 1. Quadrant I: $x \geq 0, y \geq 0$ 2. Bounded by $x=4$ : $x \leq 4$ 3. Bounded by $y=5$ : $y \leq 5$ 4. Combine: $0\leq x \leq 4$ and $0\leq y \leq 5$ Strategic Tip: Bounded regions usually imply "between" inequalities. Choice B is incorrect because it is unbounded (goes to infinity). Choice C is incorrect because it includes other quadrants. Choice D is incorrect because it excludes the boundaries (strict).

Key Steps:

•

The correct answer is $0\leq x \leq 4, 0 \leq y \leq 5$

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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