Chapter 5.7, Problem 11E

To determine

To graph:given system of linear inequalities

Explanation of Solution

Given Information: A system of linear inequalities is given by

  $\{\begin{array}{l}y>-3\\ y\ge 5x\end{array}$

Graph: The solution graph of given system of linear inequalities is as follows-

  

The shaded region is the required graph.

Interpretation:

To sketch the graph follows the following steps-

(1) Draw the lines $y=5x\text{ and }y=-3$

(2) The line $y=5x$ divides the plane into two parts first is where origin lies and second is where origin does not lie. Then check in which region does the origin (0, 0) lie by putting values in inequality $y\le 5x$ . Since this satisfies, then the region given by $y\le 5x$ is where origin lies.

(3) Similarly, the line $y=-3$ divides the plane into two parts first is where origin lies and second is where origin does not lie. Then check in which region does the origin (0, 0) lie by putting values in inequality $y>-3$ . Since this satisfies, then the region given by $y>-3$ is where origin lies.

(4) The combinations of both this region is the solution graph of system of linear inequalities

  $\{\begin{array}{l}y>-3\\ y\ge 5x\end{array}$