Chapter 5.7, Problem 21E

Solution

  

To write: a system of inequalities represented by given graph.

  $\{\begin{array}{l}y<3\\ x\ge -1\end{array}$

Given Information: a graph is given as follows-

  

Here the dotted line crosses the y-axis at (0, 3). So its equation is given by $y=3$ .

This line divides the plane into two parts, first is that where origin lie and second is that where origin doesn’t lie.

The region which contains origin is given by $y<3$ {Here equal to sign has not included because it is a dotted line and region does not contain the line}

Now the darked line crosses the x-axis at (-1, 0). So its equation is given by $x=-1$ .

This line also divides the plane into two parts, first is that where origin lie and second is that where origin doesn’t lie.

The region which contains origin is given by $x\ge -1$ {Here equal to sign has included because it is a darked line and region contains the line}

Hence the shaded region is given by set of inequalities

  $\{\begin{array}{l}y<3\\ x\ge -1\end{array}$