# NCERT Solutions for Class 9th Mathematics

## Chapter 4. Linear Equation In Two Variables

### Exercise 4.1

**Chapter 4. Linear Equation In Two Variables**

**Exercise 4.1**

**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 pen = y

Let the cost of notebook= x

Then, According To Question,

x = 2y

⇒ x - 2y = 0

**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) 2 x + 3y = 9.35**

**Solution:**

(i) 2*x *+ 3*y *= 9.35

Expressing the equation in the form of ax + by + c = 0,

∴ 2x+3y-9.35= 0

On Comparing, We have

Then, a= 2, b= 3, c= -9.3

**(ii) x – 5y – 10 = 0**

**Solution:**

(ii) *x *– 5*y *– 10 = 0

Expressing the equation in the form of ax + by + c = 0,

∴ x- 5y - 10 = 0

On Comparing, We have

Then, a= 1, b= -5, c= -10

**(iii) –2 x + 3y = 6**

**Solution:**

(iii) –2*x *+ 3*y *= 6

Expressing the equation in the form of ax + by + c = 0,

∴ -2x + 3y - 6= 0

On Comparing, We have

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

**(iv) x = 3y**

**Solution:**

(iv) *x *= 3*y*

Expressing the equation in the form of ax + by + c = 0,

∴* x - 3y= 0*

On Comparing, We have

* Then, a= 1, b= -3, c= 0*

**(v) 2 x = –5y **

**Solution:**

(v) 2*x *= –5*y *

Expressing the equation in the form of ax + by + c = 0,

∴* 2x + 5y= 0*

On Comparing, We have

* Then, a= 2, b= 5, c= 0*

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

**Solution:**

(vi) 3*x *+ 2 = 0

Expressing the equation in the form of ax + by + c = 0,

∴ 3x + 2= 0

On Comparing, We have

Then, a= 3, b= 0, c= 2

**(vii) y – 2 = 0**

**Solution:**

(vii) *y *– 2 = 0

Expressing the equation in the form of ax + by + c = 0,

∴ y-2= 0

On Comparing, We have

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

**(viii) 5 = 2 x**

**Solution:**

(viii) 5 = 2*x*

Expressing the equation in the form of ax + by + c = 0,

∴* 2x - 5= 0*

On Comparing, We have

* Then, a= 2, b= 0, c= -5*