The region represented by the inequation system \( x,y\ge 0,\ y\le 6 \) and \( x+y\ge 3 \) is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Unbounded in first quadrant
Since \( x\ge 0 \) and \( y\ge 0 \), the region lies in the first quadrant, so options (2) and (4) are ruled out.
\( y\le 6 \) is the part on or below the line y = 6.
\( x+y\ge 3 \) is the part on or above the line x + y = 3 (the origin does not satisfy it).
Nothing limits x from above: for example, every point (x, 0) with x ≥ 3 satisfies all the conditions. So the region is the strip between the lines x + y = 3 and y = 6, extending without end to the right.
Hence the region is unbounded and lies in the first quadrant.