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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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