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Chapter 5: Problem 96

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

Short Answer

Expert verified
When a system of linear inequalities has no solution, there is no common region that satisfies all inequalities in the system. Simply put, there's no intersection of the areas described by these inequalities.

Step by step solution

01

Understanding Linear Inequalities

Linear inequalities describe areas in two-dimensional space where the points within these areas satisfy the inequality condition. For instance, for the inequality \(y > 2x + 1\), any point in the plane where the y-coordinate is greater than twice the x-coordinate plus one would satisfy the condition.
02

Comprehending Systems of Linear Inequalities

A system of linear inequalities, on the other hand, is a set of two or more inequalities with the same unknowns. When graphing these inequalities on a coordinate plane, the solution to the system is the intersection area of all inequalities in the system.
03

Understanding No Solution to the System

When a system of linear inequalities has no solution, it means there is no possible region that satisfies all inequalities in the system. In other words, the inequalities don't share a common intersection.

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Most popular questions from this chapter

In Exercises 29-32, determine whether each statement makes sense or does not make sense, and explain your reasoning. I need to be able to graph systems of linear inequalities in order to solve linear programming problems.

Explain how to solve a system of equations using the addition method. Use \(3 x+5 y=-2\) and \(2 x+3 y=0\) to illustrate your explanation.

What is a linear inequality in two variables? Provide an example with your description.

In Exercises 29-32, determine whether each statement makes sense or does not make sense, and explain your reasoning. In order to solve a linear programming problem, I use the graph representing the constraints and the graph of the objective function.

When using the addition or substitution method, how can you tell if a system of linear equations has no solution? What is the relationship between the graphs of the two equations?
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