Free variable

A free variable is a variable in a mathematical expression or equation that can take any value without causing inconsistency. In the context of solving equations, some variables are dependent on others (bound variables), while free variables are not constrained by the equations and can be assigned arbitrary values. This often occurs in systems with multiple solutions or underdetermined systems. Essentially, free variables provide flexibility, representing directions in the solution space that can vary independently, allowing for multiple solutions or a continuum of possible answers.