Linear Equations in Two Variables
Chapter 4
Exercise 4.1
EX 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 = ₹ x
Let the cost of a pen = ₹ y
According to the question, Cost of a notebook = 2×Cost of a pen
x = 2×y
x = 2y
x-2y = 0
EX 4.1 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 =
(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
Solution:
(i) 2x + 3y =
⇒ (2)x + (3)y + (
a = 2 , b = 3 and c=
(ii) x –(y/5)–10 = 0
⇒ x + (-1/5) y + (10) = 0
a =1, b =-1/5 and c= -10
(iii) -2x + 3y = 6
⇒(-2)x + (3)y + (-6) = 0
a = -2, b = 3 and c = -6.
(iv) x = 3y
⇒ (1)x + (-3)y + (0) = 0
a = 1, b = -3 and c = 0.
(v) 2x = -5y
⇒ (2)x + (5)y + (0) = 0
a = 2, b = 5 and c = 0.
(vi) 3x + 2 = 0
⇒ (3)x + (0)y + (2) = 0
a = 3, b = 0 and c = 2.
(vii) y – 2 = 0
⇒ (0)x + (1)y + (-2) = 0
a = 0, b = 1 and c = -2.
(viii) 5 = 2x
⇒ 2x + 0y – 5 = 0
a = 2, b = 0 and c = -5.