In this page we have ** NCERT book Solutions for Class 8th Maths:Linear equations** for
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**Question 1**

Solve:

**Answer **

On multiplying both sides by 3*x*, we obtain

8*x* − 3 = 6*x*

*Transposing 6x to LHS and 3 to RHS*

8*x* − 6*x* = 3

2*x* = 3

Dividing 2 on both the sides

x=3/2

**Question 2 **

Solve:

**Answer **

On multiplying both sides by 7 − 6*x*, we obtain

9*x* = 15(7 − 6*x*)

9*x* = 105 − 90*x*

*Transposing 90x on LHS*

9*x* + 90*x* = 105

99*x* = 105

Dividing 99 on both the sides

x=105/99

**Question 3 **

Solve:

**Answer **

On multiplying both sides by 9(*z* + 15), we obtain

9*z *= 4(*z* + 15)

9*z *= 4*z* + 60

Transposing 4z on LHS

9*z *− 4*z* = 60

5*z* = 60

Dividing 5 on both the sides

*z* = 12

**Question 4 **

Solve

**Answer **

On multiplying both sides by 5(2 − 6*y*), we obtain

5(3*y* + 4) = −2(2 − 6*y*)

15*y* + 20 = − 4 + 12*y*

*Transposing 12y to LHS and 20 to RHS*

15*y* − 12*y* = − 4 – 20

3*y* = −24

Dividing by 3 on both the sides

*y* = −8

**Question 5**

Solve:

**Answer **

On multiplying both sides by 3(*y *+ 2), we obtain

3(7*y* + 4) = −4(*y* + 2)

21*y* + 12 = − 4*y* – 8

Transposing 4y to LHS and 12 to RHS

21*y* + 4*y* = − 8 − 12

25*y* = −20

Dividing by 25 on both the sides

y=-20/25=-4/5

**Question 6- **The ages of Hari and Harry are in the ratio 5:7. Four years from now the ratio of their ages will be 3:4. Find their present ages.

**Answer **

Let the common ratio between their ages be *x*. Therefore, Hari’s age and Harry’s age will be 5*x* years and 7*x* years respectively and four years later, their ages will be (5*x* + 4) years and (7*x* + 4) years respectively.

According to the situation given in the question,

Multiplying both the sides by 4(7x+4)

4(5x+4)=3(7x+4)

20x+16=21x+12

Transposing 20x to RHS and 12 to LHS

4=x

x=4

Hari’s age = 5*x* years = (5 × 4) years = 20 years

Harry’s age = 7*x* years = (7 × 4) years = 28 years

Therefore, Hari’s age and Harry’s age are 20 years and 28 years respectively.

**Question 7- **The denominator of a rational number is greater than its numerator by 8. If the numerator is increased by 17 and the denominator is decreased by 1, the number obtained is 3/2 . Find the rational number.

**Answer - **Let the numerator of the rational number be *x*. Therefore, its denominator will

be *x* + 8.

The rational number will be x/(x+8) According to the question

2(*x* + 17) = 3(*x* + 7)

2*x* + 34 = 3*x* + 21

34 − 21 = 3*x* − 2*x*

13 = *x*

Numerator of the rational number = *x* = 13

Denominator of the rational number = *x* + 8 = 13 + 8 = 21

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