## Chapter 8 Linear Equations in Two Variables Ex 8.1

**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)** **Solution:**

Let the cost of a notebook = ₹ x

and the cost of a pen = ₹ y

According to question,

Cost of a notebook = 2(cost of a pen)

∴ x = 2y

⇒ 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.**35¯¯¯¯¯ **(ii) x – **y5** – 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 = 9.35¯¯¯¯¯

⇒ 2x + 3y – 9..35¯¯¯¯¯ = 0

On comparing with ax+by+c = 0.

Then, the values of a = 2, b = 3 and c = 9..35¯¯¯¯¯

**(ii)** x- y5 -10= 0

On comparing with ax + by + c = 0, then the values of

a = 1, b = −15 andc = – 10

**(iii)** – 2x+ 3y = 6

⇒ -2x + 3y – 6=0

On comparing with ax + by + c = 0, then the values of a = – 2, b = 3 and c = – 6

**(iv)** x = 3y ⇒ x-3y+0=0

On comparing with ax + by + c = 0, then the values of a = 1, b = – 3 and c = 0.

**(v)** 2x = -5y

⇒ 2x + 5y + 0=0

On comparing with ax + by + c = 0, then the values of a = 2, b = 5 and c = 0.

**(vi)** 3x + 2 = 0

⇒ 3x + 0y + 2 = 0

On comparing with ax + by + c = 0, then the values of a = 3, b = 0 and , c= 2.

**(vii)** y – 2 = 0

⇒0x+y-2 = 0

On comparing with ax + by + c = 0, then the values of a = 0, b = 1 and c = – 2.

**(viii)** 5 = 2x ⇒ 2x + 0y – 5 = 0

On comparing with ax + by + c = 0, then the values of a = 2, b = 0 and c = – 5.