1
algebra

Which system of inequalities represents the shaded region bounded by y2x+1y \leq 2x + 1, yx+2y \geq -x + 2, and x3x \leq 3?

A

y2x+1,yx+2,x3y \leq 2x + 1, y \geq -x + 2, x \leq 3

B

y<2x+1,y>x+2,x<3y < 2x + 1, y > -x + 2, x < 3

C

y2x+1,yx+2,x3y \geq 2x + 1, y \leq -x + 2, x \geq 3

D

y2x+1,yx+2,y3y \leq 2x + 1, y \geq -x + 2, y \leq 3

Correct Answer: A

Choice A is the correct answer. Match each boundary line to its inequality.

  1. y2x+1y \leq 2x + 1: Solid line, shading below.
  2. yx+2y \geq -x + 2: Solid line, shading above.
  3. x3x \leq 3: Solid vertical line, shading left.
  4. Combine: The intersection of these three regions.

?�� Strategic Tip: Check the direction of shading for each line independently.

Choice B is incorrect because it uses strict inequalities (dashed lines). Choice C is incorrect because it reverses all shading directions. Choice D is incorrect because it swaps x3x \leq 3 for y3y \leq 3 (horizontal vs vertical).