Question

The region satisfying the inequalities \(y-x\geq 2, x+y\leq 5, x\geq 0\) and \(y\geq 0\) is

• A.

  

• B.

  

• C.

  

• D.

  

Hint:

Draw the lines \(y=x+2\) and \(y=5-x\) and find the region on the correct sides.

Answer 1

The Correct Option is A

Step 1: Test the origin
$(0,0)$: $0-0\ge2$ is false, so the origin side of $y=x+2$ is excluded. The region is above that line.

Step 2: Test a point
$(0,3)$: $3\ge2$ and $3\le5$, so it is inside. The region is the triangle that contains $(0,3)$ with vertices $(0,2)$, $(0,5)$, $(1.5,3.5)$. This is figure (A).

Final Answer:
The region is the triangle shown in option (A). \[ \boxed{\text{(A)}} \]