Degrees of Freedom Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

easy
How many DOF does a single equation x+y=5x + y = 5 have?

Solution

  1. 1
    n=2n = 2 variables, r=1r = 1 equation. DOF =2−1=1= 2 - 1 = 1.
  2. 2
    One free choice (pick xx, then y=5−xy = 5 - x).

Answer

11 degree of freedom
A single equation in two unknowns gives 1 DOF — geometrically, the solutions form a line. You need as many independent equations as variables for a unique solution (0 DOF).

About Degrees of Freedom

The number of independent values that remain free to be chosen after all constraints in a system have been satisfied.

Learn more about Degrees of Freedom →

More Degrees of Freedom Examples

Example 1 easy

A system has 3 variables and 2 independent equations. How many degrees of freedom?

Example 2 medium

The system [formula] has 3 equations and 3 variables. Does it have 0 degrees of freedom?

Example 4 medium

A system of 4 equations in 4 unknowns has rank 3. How many DOF?

← All Degrees of Freedom Examples Degrees of Freedom Concept