Q. 32 - Precalculus Enhanced with Graphing Utilities

Question

In Problems 23–34, graph each system of linear inequalities by hand. Verify your results using a graphing utility

$\left\{\begin{array}{l}x-4y\le 4\\ x-4y\ge 0\end{array}\right.$

Step-by-Step Solution

Answer

The graph will be 

Step 1. Graph of the line x - 4 y ≤ 4

To draw the graph of the given inequality, we will first draw the graph of $x-4y=4$

Take any arbitrary point $(0,0)$

The given inequality satisfies the point, therefore the shaded region will contain the point $(0,0)$

 

Step 2. The graph of the inequality x - 4 y ≥ 0

To graph the inequality$x-4y\ge 0$, draw the graph of $x-4y=0$.

Take any arbitrary point $(2,0)$

The given inequality do satisfy the point.

Therefore, the shaded region will contain this point.

Step 3. Final graph

The intersection of both the graphs of the line will give the final graph.