Chapter 7, Problem 75RE

To determine

Tograph: Solution set of the systems of inequalities.

Explanation of Solution

Given:

Consider the system of inequalities,

  $\begin{array}{l}\text{}2x-y<-1\\ -3x+2y>4\\ y>0\end{array}$

Graph:

Now, Plot the graph of the inequality $2x-y<-1$ .

  

Now, Plot the graph of the inequality $-3x+2y>4$ .

  

Now, Plot the graph of the inequality $y>0$ .

  

Now, Plot the graph of the inequalities.

  $\begin{array}{l}\text{}2x-y<-1\\ -3x+2y>4\\ y>0\end{array}$

  

Interpretation:

Find the vertex from

  $\begin{array}{l}\text{}2x-y=-1\\ -3x+2y=4\end{array}$

The vertex A is $\left(2,5\right)$ .

Now, find the vertex from

  $\begin{array}{l}-3x+2y=4\\ y=0\end{array}$

On solving the vertex B is $\left(-\frac{4}{3},0\right)$ .

Now, find the vertex from

  $\begin{array}{l}2x-y=-1\\ y=0\end{array}$

On solving the vertex C is $\left(-\frac{1}{2},2\right)$

Now plot the Vertex $A,B$ and $C$