The region represented by the system of inequalities \(x, y \ge 0, y \le 6, x + y \le 3\)
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → is a bounded region in the first quadrant
The conditions \(x \ge 0\) and \(y \ge 0\) keep the region in the first quadrant.
The line \(x + y = 3\) meets the axes at (3, 0) and (0, 3). The inequality \(x + y \le 3\) holds at (0, 0), so it keeps the side of the line containing the origin.
In the first quadrant, \(x + y \le 3\) gives
\(y \le 3 - x \le 3\)
so \(y \le 6\) holds automatically: it is a redundant constraint.
The region is the triangle with corners (0, 0), (3, 0) and (0, 3). It is non-empty and lies inside a finite triangle, so it is a bounded region in the first quadrant.