Problem 93 - College Algebra Essentials

Question

What is a system of linear inequalities?

Step-by-Step Solution

Answer

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 1: 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.

Step 2: 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.

Step 3: 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.