Dependent system

Definition

A dependent system is a system of linear equations in which all equations represent the same line, resulting in infinitely many solutions. This occurs when the equations are scalar multiples of one another.

5 Must Know Facts For Your Next Test

1. When graphed, the lines in a dependent system overlap completely.
2. A dependent system has infinitely many solutions because any point on the line satisfies all equations.
3. The determinant of the coefficient matrix for a dependent system is zero.
4. In reduced row-echelon form, a dependent system will have at least one row of all zeros.
5. A consistent and dependent system implies that there is no unique solution.

Review Questions

• What does it mean for a system of linear equations to be dependent?
• How can you identify a dependent system from its graph?
• What is the significance of having a row of all zeros in reduced row-echelon form?

Related terms

Consistent System:

A system of equations that has at least one solution.

Independent System: A system of linear equations with exactly one solution.

Coefficient Matrix:

A matrix derived from the coefficients of variables in a set of linear equations.