Why does the point (0,0) not lie in the solution region of x-y≥2?

Correct answer: Because 0-0≥2 is false

The governing method is substitution of a test point into the inequality. For the origin, x=0 and y=0, so x-y=0-0=0. The required condition is 0≥2, which is false because zero is less than two. Consequently, the origin is outside the half-plane represented by x-y≥2, so option A is correct. Option B is false because 0-0 equals 0, not 2. Option C is an invalid general claim; the origin is included only when it actually satisfies the given inequality. Option D is irrelevant and also incorrect: the boundary equation x-y=2 can be written as y=x-2, which is a sloping line, not a vertical line. Since the inequality is non-strict, points on the boundary would be included, but the origin is not on or in the correct side.