# Matlab Solves System of Equations

Solving a system of equations with two unknowns is a very easy *cake to bite* but when the number of unknown exceed two, solving the system of equations becomes complicated and time-consuming.

In this post, we are going to show you how you can use your computer and Matlab to solve a system of many equations.

*Caution: the following technique works only when the number of equations and the number of unknowns are the same. We will solely work will linear equations *

## Can Matlab solve a system of equations?

Yes, Matlab can help you easily solve a system of equations. Let’s jump into some examples and show you how you go about it.

### Using Matlab to Solve a system of equation with two unknowns

Let’s consider the following system of equations

The above equation can be written in the matrix form

The equation can be rewritten as

Now we are set to use Matlab!

A=[2 3;1 1]; B=[8;3]; X=inv(A)*B

*The last line does not have; at the end.*

You will see an answer like this

Which simply means that

Let’s elaborate a little more in detail here before moving forward. What we have done above is the following.

We have written the equation in the form

Where

So to have at the end the equation on the form

### Example 2: System of the equation with three unknowns

let’s consider the following system of equations

Using the same technique we used above we can write the system in the following form

Giving commands to Matlab will look like the following

A=[1 3 -2;3 2 -1;2 -1 -3]; B=[1;2;13]; X=inv(A)*B

To end up with the following result

### Final thought

If you are working on a system of equations where the number of unknowns is equal to the number of equations, this method is a good way to go. This restriction is due to the fact that using the system of matrices to solve such system of equations requires that the matrix A is invertible. If there are no possibilities of finding the *inv(A)* then this method is totally useless.