y ≤ x + 7 y ≥ - 2 x - 1 Which point x , y is a solution

Question

y &#8804; x + 7 y &#8805; - 2 x - 1 Which point x , y is a solution to the given system of inequalities in the xy -plane?

Accepted Answer

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 d x + 7 , yields 0 d 14 + 7 , or 0 d 21 , which is true. Substituting 14 for x and 0 for y in the second inequality in the given system, y e - 2 x - 1 , yields 0 e - 2 14 - 1 , or 0 e - 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 d x + 7 yields 0 d - 14 + 7 , or 0 d - 7 , which is not true. Choice B is incorrect. Substituting 0 for x and - 14 for y in the inequality y e - 2 x - 1 yields - 14 e - 2 0 - 1 , or - 14 e - 1 , which is not true. Choice C is incorrect. Substituting 0 for x and 14 for y in the inequality y d x + 7 yields 14 d 0 + 7 , or 14 d 7 , which is not true.

Question y-8804