Q. 31 - 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 

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

Step-by-Step Solution

Answer

The graph is 

Step 1. Graph of the line 2 x + y ≥ - 2

The graph of the line $2x+y=-2$ will be drawn first.

Take any arbitrary point say, $(0,0)$.

The given equation satisfies the point.

Therefore, the shaded portion will contain the point $(0,0)$

Step 2. Graph of the line 2 x + y ≥ 2

The graph of the line$2x+y=2$ will be drawn first.

Take any point say$(0,0)$

The given inequality $2x+y\ge 2$ does not satisfy the point.

Hence, it will not be included in the shaded region.

Step 3. Final graph

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