Chapter 6, Problem 22PT

To determine

Tograph : To solve the below mentioned inequalities by graphing:

  $3x-y>9$

And $y>-2x$

Explanation of Solution

Given information :

Given the two inequalities:

  $\begin{array}{l}3x-y>9\\ y>-2x\end{array}$

Graph : The graph plotted below using the inequalities:

  $\begin{array}{l}3x-y>9\\ y>-2x\end{array}$

  

Equation $3x-y>9$ is represented by light blue area in above graph.

And $y>-2x$ is represented by light green area in above graph.

Interpretation: From the above graph, we see that $3x-y>9$ is the bottom area of line $3x-y=9$ (excluding line $3x-y=9$ ) which has been represented in light blue green. And we see that $y>-2x$ is the above area of the line $y=-2x$ ( excluding the value of $y=-2x$ ) which has been represented in the light green area.

So final solution is common color area which is in dark green color. It covers the area bottom to $3x-y=9$ and above to $y=-2x$ excluding the points on lines of common color and excluding points of intersection of the lines.