NCERT Class 10 Mathematics

PAIR OF LINEAR EQUATIONS IN TWO VARIABLES 65

Equations (3) and (4) form a pair of linear equations in the general form. Now,

you can use any method to solve these equations. We get p =

1

3 and q =

1

3

Now, substituting

1

x✁ 1

forp, we have

1

x✁ 1

=

1

3

,

i.e., x – 1 = 3, i.e., x = 4.

Similarly, substituting^1
y✂ 2

for q, we get

1

y✂ 2

=

1

3

i.e., 3 = y – 2, i.e., y = 5

Hence, x = 4, y = 5 is the required solution of the given pair of equations.

Verification : Substitute x = 4 and y = 5 in (1) and (2) to check whether they are
satisfied.

Example 19 : A boat goes 30 km
upstream and 44 km downstream in
10 hours. In 13 hours, it can go
40 km upstream and 55 km
down-stream. Determine the speed
of the stream and that of the boat in
still water.

Solution : Let the speed of the boat
in still water be x km/h and speed of
the stream be y km/h. Then the
speed of the boat downstream
= (x + y) km/h,

and the speed of the boat upstream = (x – y) km/h

Also, time =

distance
speed
In the first case, when the boat goes 30 km upstream, let the time taken, in hour,
be t 1. Then

t 1 =

30

x✄y