Algebraic Method of solving Linear Equations in Two Variables

In the earlier we covered the first method of solving Linear Equations in Two Variables, i.e. the Graphical Method.

Now let move on to the second method of solving Linear Equations in Two Variables, i.e the Algebraic Method.


In a case when the point of intersection of the lines represented by two given equations has coordinates as rational numbers, graphical method is not convenient. This is when we use the a Algebraic method which is a precise method to obtain an accurate answer.

The most commonly used Algebraic Methods of solving Linear Equations in two variables are as follows:

• Method of Elimination by Substitution.
• Method of Elimination by Equating the coefficients.
• Method of Cross Multiplication.

Method of Elimination by Substitution: Elimination by substitution is the method where we express one of the variables in terms of the other variable from either of the two equations and then this expression id put in the other equation to obtain an equation in one variable.

Method of Elimination by Equating the coefficients: In this method, we eliminate one of the two variables to obtain as equation in one variable which can easily be solved.Putting the value of this variable in any one of the given equations, the value of the other variable can be obtained.