Question

The shaded region in the following figure represents a solution set of

• A. $x - y \ge 0, x + y \ge 0$
• B. $x - y \le 0, x + y \ge 0$
• C. $x - y \ge 0, x + y \le 0$
• D. $x - y \le 0, x + y \le 0$

Hint:

If the shaded region is above the line $y = x$, it implies $y \ge x$ or $x - y \le 0$.

Answer 1

The Correct Option is B

Step 1: Concept
Identify the boundaries and test points for linear inequalities.

Step 2: Meaning
The lines $x - y = 0$ and $x + y = 0$ pass through the origin. Use a test point not on the lines, like $(0, 1)$ or $(1, 0)$.

Step 3: Analysis
Looking at the shaded region (which covers the upper part of the Y-axis): For $(0, 1)$: $0 - 1 = -1 \le 0$ (Satisfies $x - y \le 0$). For $(0, 1)$: $0 + 1 = 1 \ge 0$ (Satisfies $x + y \ge 0$).

Step 4: Conclusion
The set of inequalities is $x - y \le 0$ and $x + y \ge 0$. Final Answer: (B)