Linear Equations in Two Variables (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 = $9.3\overline { 5 }$
(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 = $9.3\overline { 5 }$
⇒ (2)x + (3)y + ($-9.3\overline { 5 }$) = 0
a = 2 , b = 3 and c=  $-9.3\overline { 5 }$.

(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.

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