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# Linear Equations in Two Variables : Exercise 4.1 (Mathematics NCERT Class 9th)

Q.1       The cost of a notebook is twice the cost of a pen. Write  a linear equation in two  variables to represent this statement.
Sol.

Let the cost of notebook be  Rs x and that of a pen  be Rs y.
Since  the cost of a notebook is twice  the cost  of pen. So, the  required linear equation in two
variables to represent  the above  statement is given by
x = 2y.
$\Rightarrow$ x – 2y = 0

Q.2       Express the following linear equations in the form ax + by + c = 0 and indicate the values of a, b and c in each case :
(i)  $2x + 3y = 9.3\overline 5$
(ii) $x - {y \over 5} - 10 = 0$

(iii) – 2x + 3y = 6
(iv) x = 3y

(v) 2x = – 5y
(vi) 3x + 2 = 0

(vii) y – 2 = 0
(viii)  5 = 2x

Sol.

(i)  $2x + 3y = 9$ can be written as $2x+ 3y- 9.3\overline 5 = 0$
On comparing  it with ax + by + c = 0 , we have
a = 2, b = 3 and  $c=- 9.3\overline 5$
(ii)  On comparing  $x - {y \over 5} - 10 = 0$  with  ax  + by + c = 0, we have,

$a = 1,b = {{ - 1} \over 5}\,\,and\,\,c = - 10$
(iii)  –2x + 3y = 6 can be  written as – 2x + 3y – 6 = 0

On  comparing  it with  ax + by + c = 0 , we have
a = – 2, b = 3 and c = – 6
(iv)  x = 3y can  be written  as x – 3y = 0

On  comparing  it with  ax + by + c = 0 , we have
a = 1, b = – 3 and c = 0
(v)  2x = – 5y can be written  as  2x + 5y = 0

On  comparing  it with  ax + by + c = 0 , we have
a = 2, b = 5 and c = 0
(vi)  On  comparing  3x + 2 = 0 with  ax + by + c = 0 , we  have

a = 3, b = 0 and c = 2
(vii) On  comparing  y – 2 = 0 with  ax + by + c = 0,  we  have

a = 0 , b = 1 and c = – 2.
(viii)  5 = 2x can be written  as 2x – 5 = 0

On  comparing  with  ax + by + c = 0 , we have
a = 2, b = 0  and c = –5.
or    – 2x + 5 = 0 , we have  a = – 2, b = 0 , c  = 5

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