It depends on the specific system of linear equations. A system of three equations with three variables can have exactly one solution, infinitely many solutions, or no solution.
For example, if the system is consistent and the rank of the coefficient matrix is equal to the rank of the augmented matrix, then the system has exactly one solution.
On the other hand, if the rank of the coefficient matrix is less than the rank of the augmented matrix, then the system has no solution.
Finally, if the rank of the coefficient matrix is equal to the rank of the augmented matrix and the rank of the coefficient matrix is less than the number of variables, then the system has infinitely many solutions.
So Maureen is not correct, a system of three equations with three variables can have one, none or infinitely many solutions.