Chapter 8.9, Problem 47E

To determine

Which ordered pair is nota solution of $y\ge -9x+1$ ?

Answer to Problem 47E

The ordered pair $(-3,-1)$ is not a solution for the given inequality and option D is the correct choice.

Explanation of Solution

Given:

Four choices:

  $\text{A}\text{. (1,}-5)\text{ B}\text{. (2,1) C}\text{. (}-1,10)\text{ D}\text{. (}-3,-1)$

Calculation:

To check which ordered pair is not a solution for the given inequality, we will substitute coordinates of each given point in our inequality as shown below:

  $\begin{array}{l}y\ge -9x+1\left(\text{Given inequality}\right)\\ -5\ge -9(1)+1\left(\text{Substituting }x=1\text{and }y=-5\right)\\ -5\ge -9+1\\ -5\ge -8\end{array}$

Since thepoint $(1,-5)$ satisfies our given inequality, so the ordered pair $(1,-5)$ is a solution for the given inequality.

  $\begin{array}{l}y\ge -9x+1\left(\text{Given inequality}\right)\\ 1\ge -9(2)+1\left(\text{Substituting }x=2\text{and }y=1\right)\\ 1\ge -18+1\\ 1\ge -17\end{array}$

Since the point $(2,1)$ satisfies our given inequality, so the ordered pair $(2,1)$ is a solution for the given inequality.

  $\begin{array}{l}y\ge -9x+1\left(\text{Given inequality}\right)\\ 10\ge -9(-1)+1\left(\text{Substituting }x=-1\text{and }y=10\right)\\ 10\ge 9+1\\ 10\ge 10\end{array}$

Since the point $(-1,10)$ satisfies our given inequality, so the ordered pair $(-1,10)$ is a solution for the given inequality.

  $\begin{array}{l}y\ge -9x+1\left(\text{Given inequality}\right)\\ -1\ge -9(-3)+1\left(\text{Substituting }x=-3\text{and }y=-1\right)\\ -1\ge 27+1\\ -1\ge 28\end{array}$

Since the point $(-3,-1)$ doesn’t satisfy our given inequality, therefore, the ordered pair $(-3,-1)$ is not a solution for the given inequality.