Q. 34 - 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

$\left\{\begin{array}{l}2x+y\ge 0\\ 2x+y\ge 2\end{array}\right.$

Step-by-Step Solution

Answer

The graph of the system of inequalities is 

Step 1. Graph of the inequality 2 x + y ≥ 0

The graph of the inequality can be plotted by plotting the line$2x+y=0$

Take any arbitrary point$(2,0)$

Since the inequality $2x+y\ge 0$satisfies this point , therefore the shaded portion will consist of this point.

Step 2. Graph of the inequality 2 x + y ≥ 2

The graph of the inequality can be plotted by plotting the line $2x+y=2$

Take any arbitrary point$(0,0)$

Since, the inequality $2x+y\ge 2$does not satisfy this point. Thus, the shaded portion will not include this point.

Step 3. Final Graph

The intersection of the individual inequalities will give the graph of the given system of inequalities.