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1.1: Linear System Terminology

Definition of Linear System

A system of equations is a set or collection of equations that we will deal with all together at once. Linear Equations deal with equations that graph straight lines.

Types of Solutions for Two Equations in Two Unknowns

Type 1: Unique Solutions occur when the two graphs are lines intersecting at a single point. This point is the unique solution. Type 2: Inconsistent Solutions occur when the graphs are distinct parallel lines. Since the two lines will never intersect, there is no solution common to both equations. Type 3: Dependent Equations have infinitely many solutions. This means that the graphs are the same.

Example of a Type 1 System with a UNIQUE SOLUTION

Example of a Type 2 System with NO SOLUTION

Example of a Type 3 System with INFINITELY MANY SOLUTIONS