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Graphical Method for Finding Pair of Linear Equations in Two Variables - Pair of Linear Equations in Two Variables Class 10 Maths
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Solution of the equations graphically.
case 1: Lines representing a pair of linear equations intersect at a point

In this case point Q(4,2) is the point of intersection. It means this point is a solution for both the equations. Since lines intersect at a point, hence this is the only solution for both linear equations.
Such pair of linear equations for which if there exists a unique solution then such pair is called as consistent pair of linear equations.
case 1: Lines representing a pair of linear equations intersect at a point. In this case point (4,2) is the point of intersection. It is a solution for both the equations.

Case 2: Lines representing linear equations are parallel
In this case there is no point of intersection, hence there is no solution for such pair of linear equations.
Such pair of linear equations for which there is no solution then such pair is called as inconsistent pair of linear equations.
Case 2: Lines representing linear equations are parallel
In this case there is no point of intersection, hence there is no solution

Case 3: Lines representing pair of linear equations coincide
In this case lines coincides i.e. overlaps hence there exist infinitely many solutions. Such pair of linear equations which has infinitely many solutions is called a dependent pair of linear equations.
Case 3: Lines representing pair of linear equations coincide
In this case lines coincides hence there exist infinitely many solutions.