This statement is True.
In linear algebra, a system of linear equations can be represented in matrix form. If a system has no free variables, it indicates that all variables are leading variables, meaning that each variable corresponds to a pivot position in the matrix after row reduction to echelon form.
This scenario typically arises when the number of equations is equal to the number of variables, and the equations are consistent. Since there are no free variables, there are no degrees of freedom in choosing the values of the variables. Therefore, the solution that satisfies all the equations is unique.
In summary, the absence of free variables implies that the system cannot have infinitely many solutions or no solution at all; it will only have one specific solution, making the statement correct.