Question

The common region for the inequalities $x \geq 0, x + y \leq 1$ and $y \geq 0$, lies in

• A. IV Quadrant
• B. II Quadrant
• C. III Quadrant
• D. I Quadrant

Answer 1

Answer: (D)

I Quadrant

Answer 2

The inequalities $x \geq 0$ and $y \geq 0$ restrict the region to the first quadrant. The inequality $x + y \leq 1$ further limits the region to be on or below the line $x + y = 1$. The intersection of these conditions forms a triangle with vertices (0,0), (1,0), and (0,1), which is entirely within the first quadrant.