The best algorithm known to date was developed by Don Coppersmith and Shmuel Winograd and dates from 1990. At least n 2 operations are needed to solve a general system of n linear equations. Solving a system of linear equations has a complexity of at most O (n 3). This least squares solution can often be used as a stand-in for an exact solution. Since the measurements are not exact, it is not possible to obtain an exact solution to the system of linear equations methods such as Least squares can be used to compute a solution that best fits the overdetermined system. Each measurement is usually inaccurate and includes some amount of error. Such a system is almost always overdetermined and has no exact solution. There are examples such as geodesy where there many more measurements than unknowns. Relaxation, including the Gauss-Seidel and Jacobi methods.
So, the person solving the system of equations is looking for the values of each variable that will make all of the equations true at the same time. A "system" of linear equations means that all of the equations are true at the same time. "Linear equations" mean the variable appears only once in each equation without being raised to a power. Mathematicians show the relationship between different factors in the form of equations.