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Chapter 4 Linear Equations in Two Variables Ex 4.1 Solutions

Question - 1 : -
The cost of a notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement.
(Take the cost of a notebook to be Rs x and that of a pen to be Rs y.)

Answer - 1 : -

Let the cost of a notebook and a pen be x and y respectively.
Cost of notebook = 2 × Cost of pen
x = 2y
x − 2y = 0

Question - 2 : - Express the following linear equations in the form ax + by + c = 0 and indicate the values of a, b, c in each case:
(i)  (ii)  (iii) − 2x + 3 y = 6

(iv) x =3y (v) 2x =− 5y (vi) 3x +2 = 0

(vii) y −2 = 0 (viii) 5 = 2x

Answer - 2 : - (i) 

= 0

Comparing this equation with ax + by + c =0,

a = 2, b = 3,  

(ii) 

Comparing this equation with ax + by + c =0,

a = 1, b =

, c = −10


(iii) − 2x +3 y = 6

− 2x + 3 y − 6 = 0

Comparing this equation with ax + by + c =0,

a = −2, b = 3, c = −6


(iv) x =3y

1x − 3y + 0 = 0

Comparing this equation with ax + by + c =0,

a = 1, b = −3, c = 0


(v) 2x = −5y

2x + 5y + 0 = 0

Comparing this equation with ax + by + c =0,

a = 2, b = 5, c = 0


(vi) 3x + 2= 0

3x + 0.y + 2 = 0

Comparing this equation with ax + by + c =0,

a = 3, b = 0, c = 2


(vii) y −2 = 0

0.x + 1.y − 2 = 0

Comparing this equation with ax + by + c =0,

a = 0, b = 1, c =−2


(viii) 5 = 2x

− 2x + 0.y + 5 = 0

Comparing this equation with ax + by + c =0,

a = −2, b = 0, c =5

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