NCERT Solutions Class 9th Maths Chapter – 4 Linear Equations in Two Variables Exercise – 4.1

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).

Solution
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 and c in each case:
(i) 2x + 3y = 9.35¯

Solution – We have 2x + 3y = 9.35¯
or (2)x + (3)y + (−9.35¯¯¯ ) = 0
Comparing it with ax + by + c = 0,
we get a = 2, b = 3 and c = –9.35¯

(ii) x−y/5−10 = 0

Solution – We have x−y/5−10 = 0
or x + (- 1/5) y + (10) = 0
Comparing it with ax + by + c = 0, 
we get a =1, b = –1/5 and c = -10

(iii) – 2x + 3y = 6

Solution – We have -2x + 3y = 6
or (-2)x + (3)y + (-6) = 0
Comparing it with ax – 4 – by + c = 0,
we get a = -2, b = 3 and c = -6

(iv) x = 3y

Solution – We have x = 3y
or (1)x + (-3)y + (0) = 0
Comparing it with ax + by + c = 0,
we get a = 1, b = -3 and c = 0.

(v) 2x = -5y

Solution – We have 2x = -5y
or (2)x + (5)y + (0) = 0
Comparing it with ax + by + c = 0,
we get a = 2, b = 5 and c = 0

(vi) 3x + 2 = 0

Solution – We have 3x + 2 = 0 
or (3)x + (0)y + (2) = 0
Comparing it with ax + by + c = 0,
we get a = 3, b = 0 and c = 2

(vii) y – 2 = 0

Solution – We have y – 2 = 0
or (0)x + (1)y + (-2) = 0
Comparing it with ax + by + c = 0,
we get a = 0, b = 1 and c = -2

(viii) 5 = 2x

Solution – We have 5 = 2x ⇒ 5 – 2x = 0
or (-2)x + (0)y + (5) = 0
Comparing it with ax + by + c = 0, 
we get a = -2, b = 0 and c = 5.