 Hello and welcome to the session. In this session we will discuss about the pair of linear equations in two variables and graphical method of solving these equations. We know that two linear equations in the same two variables are called a pair of linear equations in two variables. Now the most general form of a pair of linear equations is given as a1 x plus b1 y plus c1 equal to 0 and a2 x plus b2 y plus c2 equal to 0. Where we have a1, a2, b1, b2, c1, c2 are real numbers. Also a1 square plus b1 square is not equal to 0 and a2 square plus b2 square is also not equal to 0. We have considered a pair of linear equations in two variables. Linear equations in two variables can be solved by the graphical method which we shall discuss now. We know that the graph of a pair of linear equations in two variables is represented by two lines. If these two lines intersect then we say that the system has unique solution and moreover the system is said to be consistent. As you can see these two lines of a pair of linear equations in two variables intersect at this point which would be the unique solution of the pair of linear equations. That is we have x equal to 4 and y equal to 2. So these pair of linear equations have unique solution and hence they are consistent. And if these lines coincide then we say that the system is said to have infinitely many solutions and the system is said to be dependent or consistent. And in this case each point on the line would be the solution of the pair of linear equations. This is the graph of a pair of linear equations in two variables. As you can see that the lines of both these equations are coinciding. So this pair of linear equations will have infinitely many solutions and each point on this line would be the solution for this pair of linear equations. And thus the system is dependent or you can say consistent. Next we have if these lines are parallel then we say that the system will have no solution and the system is said to be inconsistent. This is the graph of a pair of linear equations in two variables and as you can see that these two lines are parallel to each other. So this pair of equations will have no solution and thus the system is said to be inconsistent. This completes the session. Hope you have understood the concept of pair of linear equations in two variables and the graphical method of solving these equations.