Chapter 5, Problem 3CA

To determine

To fill: the blank in the system of linear inequalities with $<,\le ,>,\text{or}\ge$ so that the graph represents the system.

Answer to Problem 3CA

The linear inequalities are $y\ge 3x-2\text{and}y>-x+5$ .

Explanation of Solution

Given information:

Given graph

  

Given equation

  $\begin{array}{l}y\underset{\_}{}3x-2\\ y\underset{\_}{}-x+5\end{array}$

Calculation:

Consider the graph below.

  

Consider the below structures.

  $\begin{array}{l}y\underset{\_}{}3x-2\\ y\underset{\_}{}-x+5\end{array}$

The shaded region in the graph for both the inequalities is above the boundary line.

The boundary line of inequality with positive slope of 3 is having boundary solutions as the boundary line is represented by solid line in the graph. Hence the correct symbol for $y\underset{\_}{}3x-2$ is $\ge$ .

The boundary line of inequality with negative slope of 1 is not having boundary solutions as the boundary line is represented by dashed in the graph. Hence the correct symbol for $y\underset{\_}{}-x+5$ is >.

It means

Therefore, the linear inequalities are $y\ge 3x-2\text{and}y>-x+5$ .