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## 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 ₹x and that of a pen to be ₹y).
Let the cost of a notebook = ₹x
and the cost of a pen = ₹y
According to the question,
Cost of a notebook =2(Cost of a pen)
i.e. x = 2(y) or x = 2y or x - 2y = 0

Therefore, the linear equation for this question will be 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 = 9.3 ii) x - y/5 - 10 = 0
iii) -2x + 3y = 6
iv) x = 3y
v) 2x = -5y
vi) 3x + 2 = 0
vii) y - 2 = 0
viii) 5 = 2x

i) We have 2x + 3y = 9.3 or (2)x + (3)y + (-9.3 ) = 0
Substituting it with ax + by + c = 0, we get a = 2, b = 3 and c= -9.3 .

ii) We have x - y/5 - 10 = 0
or x + (- 15)/y + (10) = 0
Substituting it with ax + by + c = 0, we get, a = 1, b = -15 and c = -10

iii) We have -2x + 3y = 6 or (-2)x + (3)y + (-6) = 0
Substituting it with ax - by + c = 0, we get a = -2, b = 3 and c = -6.

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

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

vi) We have 3x + 2 = 0 or (3)x + (0)y + (2) = 0.
Substituting it with ax + by + c = 0, we get a = 3, b = 0 and c = 2.

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

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