Chapter 6, Problem 23PT

To determine

To graph : To solve the below mentioned inequalities by graphing:

  $y\ge 2x+3$

And $-4x-3y>12$

Explanation of Solution

Given information :

Given the two inequalities:

  $\begin{array}{l}y\ge 2x+3\\ -4x-3y>12\end{array}$

Graph : The graph plotted below using the inequalities:

  $\begin{array}{l}y\ge 2x+3\\ -4x-3y>12\end{array}$

Equation $y\ge 2x+3$ is represented by light blue area in above graph.

And $-4x-3y>12$ is represented by light green area in above graph.

Interpretation : >From the above graph, we see that $y\ge 2x+3$ is the above area of line $y=2x+3$ (including line

  $y=2x+3$ ) which has been represented in light blue green. And we see that $-4x-3y>12$ is the below area of the line $-4x-3y=12$ (excluding the value of $-4x-3y=12$ ) 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 $y=2x+3$ and above to $-4x-3y=12$ excluding the points on lines of $-4x-3y=12$ and including the points on lines of $y=2x+3$ and excluding point of intersection of the lines.