**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 + () = 0

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.