## 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 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