Activity - To find the condition of consistency

Aim- To find the condition of consistency for a pair of linear equations in two variables.
Material Required :Graph Paper , pencil , scale
Procedure
1. Take the pair of linear equations as
x + y = 4
2x + y = 6
Plot the graph of these equations.
2. Take the second pair of linear equations
x + y = 4
2x + 2y = 12
Plot the graph of these equations.
3. Take Third pair of linear equations
2x + y = 4
4x + 2y= 6
Plot the graph of these equations.
Observations
1. For intersecting lines it is observed that a1/a2 <> b1/b2
2. For coincident lines it is observed that

3. For coincident lines it is observed that


Conclusion
The first and second pair of linear equations are consistent .So the condition of consistency is
or