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 www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com

2 comments:

  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.

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

    ReplyDelete