OG详解-OG2 数学2 Q12

Choice A is correct. It’s given that the point  (x, 53) is a solution to the given system of inequalities in the xy-plane. This means that the coordinates of the point, when substituted for the variables x  and y , make both of the inequalities  in the system true. Substituting 53 for y  in the inequality y >14 yields 53 >14, which is true. Substituting 53 for y  in the inequality  4x + y <18 yields 4x +53 <18. Subtracting 53 from both sides of this inequality yields 4x <-35. Dividing both sides of this inequality by  4  yields x <-8.75. Therefore, x  must be a valueless than -8.75. Of the given choices, only -9  is less than -8.75.
Choice B is incorrect. Substituting -5  for x and  53 for y in the inequality 4x + y <18 yields 4(-5)+53 <18, or 33 <18, which is not true. Choice C is incorrect. Substituting 5  for x  and 53  for y in the inequality  4x + y <18 yields 4 (5)+53 <18, or 73 <18, which is not true. Choice D is incorrect. Substituting  9 for x  and 53 for y  in the inequality  4x + y <18 yields 4(9)+53 <18 , or 89 <18, which is not true.