Chapter 3.2, Problem 7PPS

To determine

To plot: The graph for given system of inequalities and solve

  $\begin{array}{l}x<3\hfill \\ y\ge –4\hfill \end{array}$

Explanation of Solution

Given information :

The following system of inequalities:

  $\begin{array}{l}x<3\hfill \\ y\ge –4\hfill \end{array}$

Calculation :

Let the inequalities are:

  $\begin{array}{l}x<3\mathrm{......}\left(1\right)\hfill \\ y\ge –4\mathrm{........}\left(2\right)\hfill \end{array}$

Use maple to plot the graph of the above equation.

  

To test the solution by substituting $\left(0,0\right)$ for x and y in each equation,

First, substitute the points $\left(x,y\right)=\left(0,0\right)$ in equation (1) and simplify it as follows,

  $\begin{array}{l}x<3\hfill \\ 0<3\hfill \end{array}$

This is true, means 0 is less than 3.

Now, substitute the points $\left(x,y\right)=\left(0,0\right)$ in equation (2) and simplify it as follows,

  $\begin{array}{l}y\ge –4\hfill \\ 0\ge –4\hfill \end{array}$

This is true, means 0 is greater than −4.

Hence, the graph of the inequalities overlap, both equations go towards origin and overlap. The solution is in grey color.