Problem 94 - College Algebra

Question

What is a solution of a system of linear inequalities?

Step-by-Step Solution

Answer

A solution to a system of linear inequalities is a set of values for the variables that makes every inequality in the system true at the same time. It's commonly represented as a region on a graph.

Step 1: Understanding Linear Inequalities

A linear inequality is an inequality which involves a linear function. A linear inequality contains one of the symbols <, >, ≤, or ≥. It's a way of comparing linear functions.

Step 2: Understanding Systems of Linear Inequalities

A system of linear inequalities is a set of two or more inequalities that all include the same variables. They are systems because all the inequalities must hold true at the same time.

Step 3: Understanding the Solution of a System of Linear Inequalities

The solution of a system of linear inequalities is the set of all possible values for the variables that satisfies every inequality in the system simultaneously. These solutions often form a region of points, such as a half-plane or a bounded region on a graph.

Step 4: Representing Solutions Graphically

Graphically, a solution to a system of linear inequalities is represented as the intersection of the areas represented by each inequality. This region contains all the points that satisfy all inequalities at the same time and hence, represents the solution to the system.