OG详解-OG3 数学1 Q19

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 they-coordinate of the point for x and y , respectively, in each inequality makes both of the inequalities true. Substituting the x-coordinate and they-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 -1 yields -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.