In the row echelon form of augmented matrix of $AX=B$, why is it said that you can assign arbitrary values only to columns that don't contain a pivot?

Question

Suppose we have a system of $m$ equations in $n$ unknowns, where the row reduced form of the augmented matrix has $r$ pivots. Then we will have $r$ equations with $n$ unknowns. So in order to solve the system of equations, we need to assign arbitrary values to $n-r$ variables.

However, it is said that those arbitrary values can be assigned only to columns that do not have a pivot. What is the reason?