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Chapter 9: Problem 74

What does it mean if a system of linear inequalities has no solution?

Short Answer

Expert verified
If a system of linear inequalities has no solution, it means there is no any set of values for the variables that can satisfy all inequalities in the system simultaneously.

Step by step solution

01

Understanding a System of Inequalities

A system of inequalities is a set of two or more inequalities in the same variables. The solutions to the system of inequalities are the values for the variables that satisfy all the inequalities in the system at once.
02

Possible Outcomes of a System of Linear Inequalities

When solving a system of inequalities, there are three possible outcomes: one unique solution, infinitely many solutions or no solutions.
03

What it means for a System of Inequalities to have No Solution

If a system of linear inequalities has no solution, it means that there is no any set of values for the variables that can satisfy all inequalities in the system at the same time. In the case of a two-variable system, this can be visually represented by a pair of lines on a graph that never intersect, meaning there is no single point that lies within all shaded regions simultaneously.

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Most popular questions from this chapter

How do you determine if an ordered pair is a solution of an inequality in two variables, \(x\) and \(y ?\)

Solve each inequality using a graphing utility. Graph each side separately. Then determine the values of \(x\) for which the graph on the left side lies above the graph on the right side. $$-3(x-6)>2 x-2$$

$$\text { Factor: } 25 x^{2}-81$$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The absolute value of any linear expression is greater than 0 for all real numbers except the number for which the expression is equal to \(0 .\)

Will enable you to review graphing linear functions. In addition, they will help you prepare for the material covered in the next section. In each exercise, graph the linear function. $$f(x)=-\frac{2}{3} x \text { or } y=-\frac{2}{3} x(\text { Section } 3.4, \text { Example } 4)$$
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