Graphical Method of solving Linear Equations in Two Variables

In the earlier posts we discussed about what is a Linear Equation. Further we also understood the meaning of Linear equations in Two variables and listed the various methods to solve the same.

Today let us analyze the first method that is the Graphical Method of Solving Linear Equation in two variables:

Graphical Method: The Procedure of solving a system of Linear Equations in two variables by drawing their graphs is known as Graphical Method.

The following Algorithm can be used to solve a system of Linear Equations in two variables by graphing method:-

Step 1:- Obtain the given system of Simultaneous Linear Equation in x and y.
Let the system of Linear Equation be

A₁ x +b₁ y ₌ c_{1 .....(i)}

A₂ x +b₂ y ₌ c₂ ...(ii)

Step 2:- Draw the graphs of the equations (i) and (ii) in step 1.
Let the lines l₁ and l₂ represent the graphs of (i) and (ii) respectively.

Step 3:- If the lines l₁ and l₂ intersect at a point and (a,b) are the coordinates of this point, then the given system has a unique solution given by x = a,y = b. Otherwise go to step 4.

Step 4:- If the lines l₁ and l₂ are coincident, then the system id consistent and has Infinitely many solutions. In this case, every solution of one of the equations is a solution of the system. Otherwise got to step 5.

Step 5:- If the lines l₁ and l₂ are parallel, then the given system of equations id in consistent i.e.its has no solution.