NCERT Class 9 Mathematics

76 MATHEMATICS

x + 0.y – 2 = 0. This has infinitely many
solutions. In fact, they are all of the form
(2, r), where r is any real number. Also, you
can check that every point of the form (2, r)
is a solution of this equation. So as, an
equation in two variables, x – 2 = 0 is
represented by the line AB in the graph in
Fig. 4.8.

Example 9 : Solve the equation
2 x + 1 = x – 3, and represent the solution(s)
on (i) the number line,

(ii) the Cartesian plane.

Solution : We solve 2x + 1 =x – 3, to get

2 x – x = –3 – 1

i.e., x =– 4

(i) The representation of the solution on the number line is shown in Fig. 4.9, where
x = – 4 is treated as an equation in one variable.

Fig. 4.9

(ii) We know that x = – 4 can be written as
x + 0.y = – 4

which is a linear equation in the variables
x and y. This is represented by a line. Now
all the values of y are permissible because
0.y is always 0. However, x must satisfy the
equation x = – 4. Hence, two solutions of the
given equation are x = – 4, y = 0 and x = – 4,
y = 2.

Note that the graph AB is a line parallel to
the y-axis and at a distance of 4 units to the
left of it (see Fig. 4.10).

Fig. 4.8

Fig. 4.10