**Linear Equations in Two Variables**

**Page No: 68**

**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).

**Answer**

Let the cost of pen be y and the cost of notebook be x.

A/q,

Cost of a notebook = twice the pen = 2y.

∴2y = x

⇒ x – 2y = 0

This is a linear equation in two variables to represent this statement.

**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
- (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

**Answer**

**(i) 2x + 3y = 9.35**⇒ 2x + 3y – 9.35 = 0

On comparing this equation with ax + by + c = 0, we get

a = 2x, b = 3 and c = -9.35

**(ii) x – y/5 – 10 = 0**On comparing this equation with ax + by + c = 0, we get

a = 1, b = -1/5 and c = -10

**(iii) -2x + 3y = 6**⇒ -2x + 3y – 6 = 0

On comparing this equation with ax + by + c = 0, we get

a = -2, b = 3 and c = -6

**(iv) x = 3y**⇒ x – 3y = 0

On comparing this equation with ax + by + c = 0, we get

a = 1, b = -3 and c = 0

**(v) 2x = -5y**⇒ 2x + 5y = 0

On comparing this equation with ax + by + c = 0, we get

a = 2, b = 5 and c = 0

**(vi) 3x + 2 = 0**⇒ 3x + 0y + 2 = 0

On comparing this equation with ax + by + c = 0, we get

a = 3, b = 0 and c = 2

**(vii) y – 2 = 0**⇒ 0x + y – 2 = 0

On comparing this equation with ax + by + c = 0, we get

a = 0, b = 1 and c = -2

**(viii) 5 = 2x**⇒ -2x + 0y + 5 = 0

On comparing this equation with ax + by + c = 0, we get

a = -2, b = 0 and c = 5