NCERT Class 10 Mathematics

PAIR OF LINEAR EQUATIONS IN TWO VARIABLES 41

Fig. 3.1

Both ways of representing a pair of linear equations go hand-in-hand — the
algebraic and the geometric ways. Let us consider some examples.

Example 1 : Let us take the example given in Section 3.1. Akhila goes to a fair with
Rs 20 and wants to have rides on the Giant Wheel and play Hoopla. Represent this
situation algebraically and graphically (geometrically).

Solution : The pair of equations formed is :

y =

1

2 x
i.e., x – 2y = 0 (1)

3 x + 4y = 20 (2)
Let us represent these equations graphically. For this, we need at least two
solutions for each equation. We give these solutions in Table 3.1.

Table 3.1

x 02 x 0

20

3

4

y =

2

x

01 y =

20 3

4

 x

50 2

(i) (ii)
Recall from Class IX that there are infinitely many solutions of each linear
equation. So each of you can choose any two values, which may not be the ones we
have chosen. Can you guess why we have chosen x = 0 in the first equation and in the
second equation? When one of the variables is zero, the equation reduces to a linear