Chapter 6.5, Problem 12P

Determine whether the ordered pair is a solution of the linear inequality.

$7x+2y>-5,(-1,1)$

To determine

Whether the ordered pair $\left(-1,1\right)$ is a solution of the inequality $7x+2y>-5.$

Answer to Problem 12P

The ordered pair $\left(-1,1\right)$ is not a solution of the inequality $7x+2y>-5$ .

Explanation of Solution

Given information :

Given ordered pair $\left(-1,1\right)$ and the inequality $7x+2y>-5.$

Put $\left(x,y\right)=\left(-1,1\right)$ in $7x+2y>-5$ , we get

  $\begin{array}{l}7x+2y>-5\\ \Rightarrow 7\left(-1\right)+2\left(1\right)>-5\\ \Rightarrow -7+2>-5\\ \Rightarrow -5>-5\left(\text{False}\right)\end{array}$

Thus, the inequality $7x+2y>-5$ not holds true for the ordered pair $\left(-1,1\right)$ .

Hence, the ordered pair $\left(-1,1\right)$ is not a solution of the inequality $7x+2y>-5$ .