OG详解-OG4 数学2 Q5

Choice A is correct. The given point, (8, 2), is located in the first quadrant in the xy-plane. The system of inequalities in choice A represents all the points in the first quadrant in the xy-plane. Therefore, (8, 2) is a solution to the system of inequalities in choice A. Alternate approach: Substituting 8 for x in the first inequality in choice A, x > 0, yields 8 > 0, which is true. Substituting 2 for y in the second inequality in choice A, y > 0, yields 2 > 0, which is true. Since the coordinates of the point (8, 2) make the inequalities x > 0 and y > 0 true, the point (8, 2) is a solution to the system of inequalities consisting of x > 0 and y > 0.
Choice B is incorrect. This system of inequalities represents all the points in the fourth quadrant, not the first quadrant, in the xy-plane. Choice C is incorrect. This system of inequalities represents all the points in the second quadrant, not the first quadrant, in the xy-plane. Choice D is incorrect. This system of inequalities represents all the points in the third quadrant, not the first quadrant, in the xy-plane.