Different Methods To Solve System Of Equations
In my previous articles on linear equations, you have learned how to solve linear equations by eliminating the only variable the equation contained. In this presentation I am going to explain the system of linear equations. In these types of equations, there are more than one variable involve and more than one equation to solve as well.
Solving linear equations in one variable is isolating the variable but solving system of linear equations is not only isolating the variable at one side but solving all the given variables in all the equations simultaneously. In these types of equations, there may be two equations with two variables or three equations with three variables as shown below.
System of two linear equations with two variables "x" and "y" is given below:
3x + 5y = 2
2x - 3y = - 5
Also there is possibility of a system of three linear equations with three different variables.
This system of equations is a grade eleven level and a higher algebra topic. But the method to solve is similar the method above. Below is an example equations having three variables "x", "y" and "z":
2x + y + 2z = 1
x + y + z = 1
3x - y + 2z = 0
Above was the introduction to different system of linear equations and two very common types of systems we have discussed. Next 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 you with these methods and explain them one by one in my coming articles. Below is the list of all three methods to solve system of equations.
1. Graphing method to solve system of linear equations: This method involves drawing the graph for each equation and analyzes the graph to find the solution. Graphing can be further done by the following three ways:
Graphing by tabular method or graphing by intercepts or graphing of equations by finding the "slope" and "y-intercept".
2. Substitution method: This method involves finding the value of one variable in the form of other variable in substitute this value into other equation in the system.
3. Elimination method: This is the most common and easiest method to solve system of equations. In this method the coefficients of the same variable in all the equations made same and then equations are subtracted to get rid of this variable and the resulting equation is solved to find the value of the other variable.
