# MATLAB Programs for Simultaneous Equations

We have seen how to find the root of the equation, Integration,Ordinary Differential Equations,etc using MATLAB software. In this post we will see the programs for simultaneous equations.
A set of equations is known as system of simultaneous equations.

### Engineering Applications of Simultaneous Equations:

Linear algebraic system of equations occurs in many applications. The simplest case is two equations with two unknown. But there are few cases where a system is with ten, fifty or even hundred equations and unknowns.
Varoius methods to solve linear algebraic equations are given below:
For solving the simultaneous equations, they are classified in two methods i.e. direct method and other is iterative method.
Direct method and iterative method are further classified in two groups.
Direct method is classified as solution by Gauss-Elimination method and Thomas Algorithm method.
Similarly, iterative method is classified as solution by Gauss-Elimination method and Gauss-Seidal relaxation method.
In direct method, the elimination approach is taken to achieve the solution. The solution that is obtained is the exact solution.
In iterative method, the iterative approach is taken to achieve the solution. The solution obtained is approximate solution.
Here, we are providing MATLAB program files which includes the program of different methods with their solutions. Using the outputs obtained you can check the accuracy of the problem,

Gauss Elimination with partial pivoting

Gauss Elimination method

Gauss-Seidal with accuracy

Gauss-Seidal with iteration

Gauss-Seidal with pivoting

Gauss-Seidal with relaxation

Tridiagonal matrix algorithm method