Chapter 11: Q. 9 (page 772)

True or False:
The graph of a system of inequalities must have an overlapping region.

Short Answer

Expert verified

The given statement is false.

Step by step solution

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,

$\{\begin{cases} x + y > 4 \\ x + y < 1 \end{cases}$

Plot the inequalities,

Hence, the system of inequalities does not always overlap.

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True or False:
The graph of a system of inequalities must have an overlapping region.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Reason for being false.

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True or False:The graph of a system of inequalities must have an overlapping region.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Reason for being false.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Calculus

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Logic and Functions

Study anywhere. Anytime. Across all devices.

True or False:
The graph of a system of inequalities must have an overlapping region.