Chapter 6.6, Problem 5P

Open-Ended When can you say that there is no solution for a system of linear inequalities? Explain your answer and show with a system and graph.

To determine

To explain when there is no solution for given system of linear inequalities.

Explanation of Solution

When the two linear inequalities have to intersection on the graph, then we can say that the system of linear inequalities have no solution.

Let us take two inequalities,

  $\begin{array}{l}x\ge 1\\ x\le -1\end{array}$

Now plot them on graph we get,

  

Blue region is $x\le -1$

Red region is $x\ge 1$

As there is no intersection therefore there is no solution.