Suppose the coefficient matrix of a linear system of three equations in three variables has a pivot in each column. Explain why the system has a unique solution. A system of linear equations with fewer equations then unknowns is called an underdetermined system. Suppose that such a system happens to be consistent. Explain why there must be infinitely many solutions to the system. A system of linear equations with more equations then unknowns is called an overdetermined system. Can such a system be consistent? Illustrate your answer with a specific example of a system with three equations in two unknowns.