Wednesday, July 4, 2012

Linear Equations - Graphical Solution

If a, b, and c are real numbers (and if a and b are not both equal to 0 simultaneously) then ax + by +c = 0 is called a linear equation in two variables. (The “two varaibles” are the x and the y.) The numbers a and b are called the coe´Čâcients of the x and y respectively while c is called the constant coefficient. 

A pair of linear equations in two variables can be represented, and solved, by the:
                  (i) graphical method                        (ii) algebraic method 
Here we will discuss only graphical method of solving pair of linear equations. 

The graph of a pair of linear equations in two variables is represented by two lines. 
  • the lines may intersect , in this case the pair of equations has a unique solution and the pair of equations is consistent. 
  • the lines may be coincident , in this case there are infinitely many solutions , the pair of equations is dependent (consistent)
  • the lines may be parallel, in this case the pair of equations has no solution, the pair of equations is inconsistent.
If a1x+b1y+c1=0 and a2x+b2y+c2=0 are two linear equations ,then the lines representing them will be
  • intersecting if , a1/a2 ≠ b1/b2 
  • coincident if , a1/a2=b1/b2 = c1/c2 
  • parallel if , a1/a2 = b1/b2 ≠ c1/c2 
In the following applet enter equations in two input boxes with different values of coefficients of x y and constant coefficients.

This is a Java Applet created using GeoGebra from - it looks like you don't have Java installed, please go to


  1. Linear equations can be solved by many methods but graphical method is best for it.It illustrates more than other methods and easy to learn.

  2. Thanks a lot :) It helped me a lot :)