OG详解-OG8 数学1 Q22

Choice D is correct. A point (x, y) is a solution to a system of inequalities in the xy-plane if substituting the x-coordinate and the y-coordinate of the point for x and y, respectively, in each inequality makes both of the inequalities true. Substituting the x-coordinate and the y-coordinate of choice D, 14 and 0, for x and y, respectively, in the first inequality in the given system, y≤x+7, yields 0 ≤ 14+7, or 0≤21, which is true. Substituting 14 for x and 0 for y in the second inequality in the given system, y≥-2x-1, yields 0≥-2(14) -1, or  0≥-29, which is true. Therefore, the point (14, 0) is a solution to the given system of inequalities in the xy-plane.
Choice A is incorrect. Substituting -14 for x and 0 for y in the inequality y ≤x+7 yields 0 ≤-14+7, or 0 ≤-7, which is not true. Choice B is incorrect. Substituting 0 for x and -14 for y in the inequality y ≥-2x-1yields -14≥-2(0) -1, or -14 ≥-1, which is not true. Choice C is incorrect. Substituting 0 for x and 14 for y in the inequality y ≤x+7 yields 14 ≤ 0+7, or 14 ≤ 7, which is not true.