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 coefficients 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