The current published story of 'Goldilocks and the Three Bears' has been modified several times since the original tale was told in the early 1800's. This paper will modify the story again, but using matrices. All solutions of linear systems have either a common solution, or not. In many courses, no further work is completed if no common solution exists. Based on the solution(s) to a linear system, there are three system models to consider. The 'just-right' one solution, the 'too hot' many solutions, and the 'too cold' optimal solution not likely satisfying any equation. This paper will present the solving of a linear system using the adjoint matrix. If no common solution exists, the corresponding optimal solution will be determined. For a linear system with three or less equations, the solution can certainly be completed using 'pencil-and-paper' methods. For a larger number of equations, software methods will be used.