# System of Two Linear Equations in Matrix Form

In this tutorial we shall represent equations of straight lines into matrix form; first we will discuss one linear equation in matrix form.

One Linear Equation:
Consider the equation of straight line is given as

Equation (i) is a linear equation in two variables $x$ and $y$ can be written as in matrix form as follows:
Now equation (i) becomes

It can be further written as

Where $A = \left[ {\begin{array}{*{20}{c}} a&b \end{array}} \right]$ is the coefficient matrix, $X = \left[ {\begin{array}{*{20}{c}} x \\ y \end{array}} \right]$ is variable matrix and $C = \left[ { - c} \right]$ is the constant matrix.
Now we shall discuss system of two equations in matrix form

A System of Two Linear Equations:
Consider the system of two equations of straight lines are given as

Equation (i) and (ii) are linear equations in two variables $x$ and $y$ can be written as in matrix form as follows:
Now equation (i) becomes

It can be further written as

Where $A = \left[ {\begin{array}{*{20}{c}} {{a_1}}&{{b_1}} \\ {{a_2}}&{{b_2}} \end{array}} \right]$ is the coefficient matrix, $X = \left[ {\begin{array}{*{20}{c}} x \\ y \end{array}} \right]$ is variable matrix and $C = \left[ {\begin{array}{*{20}{c}} { - {c_1}} \\ { - {c_2}} \end{array}} \right]$ is the constant matrix.