When two lines are drawn in the same plane, only one of the following three situations is possible:
i) The two lines may intersect at one point.

ii) The two lines may not intersect i.e., they are parallel.
iii) The two lines may be coincident. (actually both are same)

Let us write the equations in the first example in terms of x and y, where x is the cost of a notebook and y is the cost of a pen. Then, the equations are 3x + 2y = 80 and 4x + 3y = 110.

After plotting the above points in the Cartesian plane, we observe that the two straight lines are intersecting at the point (20, 10).
Substituting the values of x and y in the equations we get 3(20) + 2(10) = 80 and 4(20) + 3(10) = 110. Showing the both the equations satisfying.
Thus, as determined by the graphical method, the cost of each book is `20 and of each pen is `10. Recall that we got the same solution using the model method.
Since (20, 10) is the common point, there is only one solution for this pair of linear equations in two variables. Such equations are known as consistent and independent pairs of linear equations. They will always have a unique solution.



page no:81

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