This **linear equations calculator** can help you solve any system having 2 or 3 equations/unknown variables by specifying their coefficients & terms within two matrices.

## How does this linear equations calculator work?

A system of linear equations, often called as linear system consists of a collection of linear equations having the same set of unknown variables to be determined while taking into account that the solution has to ensure that all the equations are simultaneously satisfied.

This *linear equations calculator* requires inputting the coefficients and the independent terms within two matrices having the following format:

In case of a system consisting of 2 equations, the two matrices to be filled in are:

In case of one made of 3 equations, the two matrices to be provided are:

The matrix equation is **A*X = B.**

Where:

A represents the **coefficient matrix**.

B is the matrix of the **free/constant terms matrix**.

X refers to the **vector of variables**.

## Example of a calculation

Let’s take the following example:

- 11x + 2y + 3 z = 4

4x + 3y + 6z = 5

7x + 8y + 9z = 6

Will result in:

x = -3/23 = -0.

*y* = -9/23 = -0.

*z* = 77/69 = 1.11594202899