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Chapter 5: Problem 93

What is a system of linear inequalities?

Short Answer

Expert verified
A system of linear inequalities is a collection of two or more linear inequalities with the same set of variables. Solving such a system indicates finding all the values of the variables that satisfy all the inequalities at once. It often corresponds to a region of the coordinate plane as the solution.

Step by step solution

01

Definition of Linear Inequalities

A linear inequality is an inequality which involves a linear function. A linear inequality looks like a linear equation, with the '=' replaced by '>', '<', '>=', or '<='. For example, \(y > 2x + 1\) is a linear inequality.
02

Understanding the System of Linear Inequalities

A system of linear inequalities is a set of linear inequalities that are considered simultaneously. To solve the system means to find all values of the variables that satisfy all the inequalities in the system. It often represents a region of the coordinate plane that is bounded by lines.
03

Example of a System of Linear Inequalities

For example, a system of linear inequalities can be: \(y > 2x + 1\) and \(y \leq x - 1\). The task here is to find the set of points (x, y) that satisfy both inequalities.

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Most popular questions from this chapter

write the partial fraction decomposition of each rational expression. $$ \frac{4 x^{2}-7 x-3}{x^{3}-x} $$

Find the partial fraction decomposition of $$ \frac{4 x^{2}+5 x-9}{x^{3}-6 x-9} $$

perform each long division and write the partial fraction decomposition of the remainder term. $$ \frac{x^{4}+2 x^{3}-4 x^{2}+x-3}{x^{2}-x-2} $$

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 find the partial fraction decomposition of a rational expression with a repeated linear factor in the denominator.
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