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## Methods To Solve System Of Linear Equations

**Different methods to solve the system of equations**

In my previous articles on linear equations, you learned how to solve linear equations by eliminating the only variable that contains the equation. In this presentation I will explain the system of linear equations. In this type of equation, there is more than one variable involved and more than one equation to solve as well.

Solving linear equations in one variable is isolating the variable, but solving a system of linear equations is not only isolating the variable on one side, but solving all the given variables in all the equations simultaneously. In these types of equations, there can be two equations with two variables or three equations with three variables, as shown below.

Below is a system of two linear equations with two variables “x” and “y”:

**3x + 5y = 2**

**2x – 3y = – 5**

There is also the possibility of a system of three linear equations with three different variables.

This system of equations is an eleventh grade level and higher algebra topic. But the method to solve is similar to the above method. Below is an example of equations with three variables **“x”, “y” and “z”:**

**2x + y + 2z = 1**

**x + y + z = 1**

**3x – y + 2z = 0**

Above was the introduction to different systems of linear equations and two very common types of systems we discussed. Below are the ways to solve the system of linear equations. There are three very common methods to solve and in this article I will introduce these methods and explain them one by one in my next articles. Below is a list of the three methods for solving the system of equations.

1. **Graphical method to solve the system of linear equations:** This method involves drawing the graph of each equation and analyzing the graph to find the solution. The graph can be made in the following three ways:

Graphing by tabular method or graphing by intercepts or graphing equations by finding the “slope” and “y-intercept”.

2. **Replacement method:** This method involves finding the value of one variable in the form of another variable to substitute that value into another equation of the system.

**3. ****Removal Method: **This is the most common and easiest method to solve a system of equations. In this method the coefficients of the same variable in all equations are made equal and then equations are subtracted to get rid of that variable and the resulting equation is solved to find the value of the other variable.

So there are three very common methods to solve the system of linear equations and we will explore them one by one in my next articles.

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