Q. 9 - Precalculus Enhanced with Graphing Utilities

Question

True or False:

The graph of a system of inequalities must have an overlapping region.

Step-by-Step Solution

Answer

The given statement is false.

Step 1. Given information.

Consider the given statement,

"The graph of a system of inequalities must have an overlapping region."

We know, that the graph of a system of inequalities must have an overlapping region is false.

The system of inequalities does not always overlap.

Step 2. Reason for being false.

Consider the system of inequalities,

$\left\{\begin{array}{l}x+y>4\\ x+y<1\end{array}\right.$

Plot the inequalities,

Hence, the system of inequalities does not always overlap.