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**Mathsight Class 6 Solutions Chapter 9 Linear Equations**

Welcome to NCTB Solutions. Here with this post we are going to help 6th class students to solve MathSight Class 6 Mathematics Book, Chapter 9, Linear Equations. Here students can easily get all the exercise questions solution for Chapter 9, Linear Equation Exercise 9.1, 9.2 and 9.3

**Linear Equations Exercise 9.1 Solution : **

**Question no – (1)**

**Solution :**

**(a)** Y

**(b)** N

**(c)** N

**(d)** N

**Question no – (2)**

**Solution : **

**(a)** x – 3 = 9

**(b)** x + y = 11

**(c)** 10 – q = 7

**(d)** 3 × (2x) = 12

**(e)** c/5 = -1

**(f)** x + 3x = 12

**Question no – (3)**

**Solution : **

193 – 7x = 46

**Question no – (4)**

**Solution :**

250 – [x + (250-x)/2] = 50

**Linear Equations Exercise 9.2 Solution : **

**Question no – (1)**

**Solution :**

**(a)** L.H.S

= 60/5

= 12. ….[Proved]

**(b)** L.H.S

= 3.(1) – 7

= -4 ….[Proved]

**(c)** L.H.S

= 8- 3/3

= 8 – 1

= 7 ….[Proved]

**Question no – (2)**

**Solution :**

**(a)** 7 – 3x = 4

Or, 7 – 3x – 7 = 4 – 7

Or, – 3x = -3

Or, x = 1

**(b)** 15/x – 1 = 2

Or, 15/x – 1 + 1 = 2 + 1

Or, 15/x = 3

Or, x = 15/3 = 5

**(c)** 3x – 2x = 3

Or, x = 3

**(d)** 2 (p – 3) = 6

Or, 2p – 6 = 6

Or, 2p – 6 + 6 = 6 + 6

Or, 2p = 12

Or, p = 12/2 = 6

**(e)** 12 – t = t – 2

Or, t + t = 12 + 2

Or, 2t = 14

Or, t = 14/2

Or, t = 7

**(f)** 2x – 5 = 15

Or, 2x – 5 + 5 = 15 + 5

Or, 2x = 20

Or, x = 20/2

= 10

**(g)** 2 (3m – 1) = m + 10

Or, 6m – 2 = m + 10

Or, 6m – m = 10 + 2 = 12

Or, 5m = 12

Or, m = 12/5

**Question no – (3)**

**Solution :**

**(a)** 3 – 4x = – 13

Or, 4x = 13 + 3

Or, 4x = 16

Or, x = 16/4 = 4

**(b)** 6y – 10 = 34

Or, 6y = 34 + 10 = 44

Or, y = 44/6 = 22/3

**(c)** x/2 – 5 = x + 11

Or, x/2 – x = 11 + 5

Or, x – 2x/2 = 16

Or, -x/2 = 16

Or, x = -(16 × 2) = – 32

**(d)** 2 (x – 1) = 3x + 5

Or, 2x – 1 = 3x + 5

Or, 3x – 2x = -5 -1

Or, x = -6

**Linear Equations Exercise 9.3 Solution : **

**Question no – (1)**

**Solution :**

Let, the Number = x

According to question

2x + 21 = 51

Or, 2x = 51 – 21 = 30

Or, x = 30/2

∴ x = 15

Therefore, the required number will be 15

**Question no – (2)**

**Solution :**

Let, one number = x

Another number = x + 2

According to question,

x + (x + 2) = 22

Or, 2x = 22 – 2 = 20

Or, x = 20/2 = 10

∴ Number are x = 10, x + 2 = 10 + 2 = 12

Hence, the required numbers are 10 and 12

**Question no – (3)**

**Solution :**

Let, total number of students = x

According to question –

X – x/3 = 36

Or, 3x – x/3 = 36

Or, 2x = 36 × 3

Or, x = 36 × 3/2

Or, x = 54

**Question no – (4)**

**Solution :**

Let, the number = x

13 + 2x = 37

Or, 2x = 37 – 13 = 24

Or, x = 24/2 = 12

**Question no – (5)**

**Solution :**

Let, Kamla son’s age = x

∴ Kamla age = 4X

5 years ago Kamla age = 4x – 5

5 years ago kgamla son’s age = x – 5

According to question,

X – 5 = 1/2

Or, x = 1/2 + 1/5

= 1 10/2

= 11/2 year

∴ Kamla’s age = 4 × 11/2

= 22 years.

Therefore, Kalma’s age now will be 22 years.

**Question no – (6)**

**Solution :**

Let, the number = x

According to question

x/5 – 5 = -2

Or, x/5 = -2 + 5 = 3

Or, x = 3 × 5 = 15

Hence, 15 will be the required number.

**Question no – (7)**

**Solution :**

Let, original amount = x

According to question

X + 51 = 4x

Or, 4x – x = 51

Or, 3x = 51

Or, x = 51/3

∴ x = 17 Rs

Therefore, the original amount of her purse was Rs 17.

**Question no – (8)**

**Solution : **

Let, green ball’s wf = x

Blue ball’s wf,

= 1 1/3 × x

= 4x/3

**Previous Chapter Solution : **