# Class 9 RD Sharma Solutions – Chapter 13 Linear Equation in Two Variable – Exercise 13.1

**Question 1: 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 = 12 **

**(ii) x – y/2 – 5 = 0 **

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

**(iv) 3x = -7y **

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

**(vi) y – 5 = 0**

**(vii) 4 = 3x **

**(viii) y = x/2**

**Solution:**

(i) -2x + 3y = 12Rearranging,

– 2x + 3y – 12 = 0

On comparing with the given form of linear equation, ax + by + c = 0,

We get,

a = – 2

b = 3

c = -12

(ii) x – y/2 – 5 = 0On comparing with the given form of linear equation, ax + by + c = 0,

We get,

a = 1

b = -1/2

c = -5

(iii) 2x + 3y = 9.35Rearranging, 2x + 3y – 9.35 = 0

On comparing with the given form of linear equation, ax + by + c = 0,

We get,

a = 2

b = 3

c = -9.35

(iv) 3x = -7yRearranging, 3x + 7y + 0 = 0

On comparing with the given form of linear equation, ax + by + c = 0,

We get,

a = 3

b = 7

c = 0

(v) 2x + 3 = 0Rearranging, 2x + 0y + 3 = 0

On comparing with the given form of linear equation, ax + by + c = 0,

We get,

a = 2

b = 0

c = 3

(vi) y – 5 = 0Rearranging, 0x + y – 5 = 0

On comparing with the given form of linear equation, ax + by + c = 0,

We get,

a = 0

b = 1

c = -5

(vii) 4 = 3xRearranging, 3x + 0y – 4 = 0

On comparing with the given form of linear equation, ax + by + c = 0,

We get,

a = 3

b = 0

c = -4

(viii)y = x/2Rearranging, x – 2y +0 = 0

On comparing with the given form of linear equation, ax + by + c = 0,

We get,

a = 1

b = -2

c = 0

**Question 2: Write each of the following as an equation in two variables:**

**(i) 2x = -3 **

**(ii) y=3 **

**(iii) 5x = 7/ 2 **

**(iv) y = 3/2x**

**Solution:**

(i)2x = -3Rearranging,

2x + 3 = 0

Now adding ‘y’ term,

2x + 0.y + 3 = 0

Required equation is,

2x + 0.y + 3 = 0

(ii)y = 3Rearranging,

y – 3 = 0

Now adding ‘x’ term,

0.x + y – 3 = 0

Required equation is,

0.x + y – 3 = 0

(iii) 5x = 7/2Rearranging,

10x = 7,

or 10x – 7 – 0;

Now adding ‘y’ term,

10x +0.y – 7 = 0

Required equation is,

10x + 0.y – 7 = 0

(iv) y = 3/2 xRearranging,

2y = 3x

or 3x – 2y = 0

Now adding the constant term,

3x – 2y + 0 = 0

Required equation is,

3x – 2y + 0 = 0

**Question 3: The cost of ball pen is Rs 5 less than half of the cost of fountain pen. Write this statement as a linear equation in two variables.**

**Solution:**

Let the cost of a ball pen and fountain pen be x and y respectively.

According to the question the following equation can be formed,

x = y/2 − 5

or x = (y – 10)/2

or 2x = y – 10

or 2x – y + 10 = 0

The required linear equation will be

2x – y + 10 = 0.

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