Chapter 3.7, Problem 36WE

To determine

To graph: The given system of inequalities.

Explanation of Solution

Given information: System of inequalities is:

  $\begin{array}{l}x\ge 0\\ y\ge 0\\ x-y+2>0\\ 2x-y<2\end{array}$

Graph:

The inequalities $x\ge 0andy\ge 0$ tell that the graph of the system is contained in first quadrant including the solid boundaries $x=0andy=0$ .

Transforming the other two inequalities,

  $\begin{array}{l}x-y+2>0\\ \Rightarrow -y>-x-2\\ \Rightarrow y<x+2\\ and\\ 2x-y<2\\ \Rightarrow -y<-2x+2\\ \Rightarrow y>2x-2\end{array}$

Thus, the solution region is below & not including the boundary line $y=x+2$ and above & not including the boundary line $y=2x-2$ .

The graph of the system is the orange colored region in the first quadrant below & not including the line $y=x+2$ and above & not including the line $y=2x-2$ .