y > 14 4 x + y < 18 The point x , 53 is a solution to the system

Question

y &#62; 14 4 x + y &#60; 18 The point x , 53 is a solution to the system of inequalities in the xy -plane. Which of the following could be the value of x ?

Accepted Answer

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 4 x + y < 18 yields 4 x + 53 < 18 . Subtracting 53 from both sides of this inequality yields 4 x < - 35 . Dividing both sides of this inequality by 4 yields x < - 8.75 . Therefore, x must be a value less 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 4 x + 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 4 x + 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 4 x + y < 18 yields 4 9 + 53 < 18 , or 89 < 18 , which is not true.

Question y-62-1