Independent system

Definition

An independent system is a set of linear equations with exactly one solution. The graphs of these equations intersect at a single point.

5 Must Know Facts For Your Next Test

1. An independent system has a unique solution, typically represented as $(x, y)$.
2. The determinant of the coefficient matrix for an independent system is non-zero.
3. Graphically, the lines representing each equation in an independent system intersect at exactly one point.
4. In an independent system, the equations are not multiples of each other.
5. The solution to an independent system can be found using methods such as substitution, elimination, or matrix operations.

Review Questions

• What characteristic distinguishes an independent system from other types of systems?
• How can you determine if a given set of linear equations forms an independent system using their graphs?
• What does it mean if the determinant of the coefficient matrix in a system of equations is zero?

Related terms

Dependent System: A set of linear equations that have infinitely many solutions because they represent the same line.

Inconsistent System: A set of linear equations with no solutions because their graphs are parallel lines that never intersect.

Determinant: A scalar value that can be computed from the elements of a square matrix and determines whether the matrix has an inverse.