8

Set 2: Linear Inequalities (Advanced)

Explanation

Answer: A

Which system of inequalities represents the shaded region in the first quadrant bounded by x<4x < 4 and y<3y < 3?

A.

x<4,y<3,x>0,y>0x < 4, y < 3, x > 0, y > 0

✓ Correct
B.

x>4,y>3,x>0,y>0x > 4, y > 3, x > 0, y > 0

C.

x<4,y<3x < 4, y < 3

D.

x4,y3x \leq 4, y \leq 3

Detailed Explanation

Choice A is correct. Choice A is the correct answer. "First quadrant" implies x>0x > 0 and y>0y > 0. 1. First Quadrant: x>0x > 0 and y>0y > 0 2. Bounded by: x<4x < 4 (left of vertical line 4) and y<3y < 3 (below horizontal line 3) 3. Combine: All four conditions must be met. Strategic Tip: Always check for quadrant constraints (x>0,y>0x>0, y>0) in geometry problems. Choice B is incorrect because it shades the wrong directions (right and up). Choice C is incorrect because it includes regions in other quadrants (negative x and y). Choice D is incorrect because it uses inclusive inequalities (solid lines) when strict (<<) were specified, and misses quadrant constraints.

Key Steps:

The correct answer is x<4,y<3,x>0,y>0x < 4, y < 3, x > 0, y > 0

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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