Chapter 5, Problem 8CA

To determine

To find: the pair which ordered is a solution of the linear inequality whose graph is shown.

Answer to Problem 8CA

The correct solution is $\left(-1,-1\right)$ .

Explanation of Solution

Given information:

Given pair

  $\left(1,1\right)$

  $\left(-1,1\right)$

  $\left(-1,-1\right)$

  $\left(1,-1\right)$

Given graph

  

Calculation:

Consider the graph below.

  

The boundary line passes through the point $\left(-1,0\right)$ and hence $y$ intercept is $-1$ . The slope of the boundary line is $-2$ . Therefore the linear inequality is

  $\begin{array}{l}y<-2x-1\text{Use}\text{slope}\text{intercept}\text{formul}a.\\ \text{the}\text{boundary}\text{line}\text{values}\text{are}\text{not}\text{in}\text{the}\text{solution}\text{set}\text{.}\\ \text{Hence}\text{use<}\text{symbol}\end{array}$

Substitute the points $\left(1,1\right),\left(-1,1\right),\left(-1,-1\right),\left(1,-1\right)$ in $y<-2x-1$ and verify.

  $\begin{array}{c}y<-2x-1Writetheinequality\\ 1<-2\left(1\right)-1Substitute\left(1,1\right).Statementisnottrue\\ 1<-2\left(-1\right)-1Substitute\left(-1,1\right).Statementisnottrue\\ -1<-2\left(-1\right)-1Substitute\left(-1,-1\right).Statementistrue\\ -1<-2\left(1\right)-1Substitute\left(1,-1\right).Statementisnottrue\end{array}$

The ordered pair $\left(x,y\right)=\left(-1,-1\right)$ represents the solution of linear inequality $y<-2x-1$ .

Therefore, the correct solution is $\left(-1,-1\right)$ .