Gauss, Gauss-Jordan elimination:
For 2 × 2 systems of equations, there are well-defined, easy solution techniques. Though, for the larger systems of equations, finding solutions is often not as clear-cut.
The two related techniques of solving systems of the linear equations will be explained here: Gauss elimination, and Gauss-Jordan elimination. They both depend on the observation that the systems of equations are equal if they have similar solution set. Performing simple operations on the rows of a matrix is also known as Elementary Row Operations (EROs), which result in equivalent systems.