What is the common region of (x+y≤5) and (x+y≥2)?

Correct answer: strip between two parallel lines

The governing concept is the graphical solution of simultaneous linear inequalities. The boundary equations are x+y=5 and x+y=2. Since both have the same coefficients of x and y but different constants, they are distinct parallel lines. The inequality x+y≤5 represents the half-plane on or below one line, while x+y≥2 represents the half-plane on or above the other. Their intersection consists of all points satisfying 2≤x+y≤5, which is the closed strip between the two parallel lines. The boundaries are included because both signs are non-strict. Therefore option A is correct. Option B gives only a boundary line, option C is false because many points satisfy both inequalities, and option D has no connection with these linear boundaries.