# NCERT Solutions for Class 10 Maths Chapter 3 - Pair of Linear Equations in Two Variables Exercise 3.3

NCERT Solutions for Class 10 Maths Chapter 3 Exercise 3.3 contains the solutions to all the questions provided on page number 53 of the textbook. The NCERT Solutions Class 10 Maths contains step-wise solutions to all the Maths problems. These are very beneficial for the students while preparing for board examinations.

NCERT Solutions Class 10 Maths Chapter 3 â€“ Pair of Linear Variables is an important topic for the examinations and should be dealt with in complete detail. Practising the exercises repeatedly will help the students score well in the board examinations. NCERT Solutions are the best guides for students studying with detailed study material, including important topics. Accurate solutions are provided by the subject experts here. The experts have tried to include all that is important. The students can refer to the solutions for a better understanding of the topic.

## Access other exercise solutions of Class 10 Maths Chapter 3 â€“ Pair of Linear Equations in Two Variables

Exercise 3.1 Solutionsâ€“ 3 Questions
Exercise 3.2 Solutionsâ€“ 7 Questions
Exercise 3.4 Solutionsâ€“ 2 Questions
Exercise 3.5 Solutionsâ€“ 4 Questions
Exercise 3.6 Solutionsâ€“ 2 Questions
Exercise 3.7 Solutionsâ€“ 8 Questions

### Access answers of Maths NCERT Class 10 Chapter 3 â€“ Pair of Linear Equations in Two Variables Exercise 3.3

1. Solve the following pair of linear equations by the substitution method.

(i) x + y = 14

x â€“ y = 4

(ii) s â€“ t = 3

(s/3) + (t/2) = 6

(iii) 3x â€“ y = 3

9x â€“ 3y = 9

(iv) 0.2x + 0.3y = 1.3

0.4x + 0.5y = 2.3

(v) âˆš2 x+âˆš3 y = 0

âˆš3 x-âˆš8 y = 0

(vi) (3x/2) â€“ (5y/3) = -2

(x/3) + (y/2) = (13/6)

Solutions:

(i) Given,

x + y = 14 and x â€“ y = 4 are the two equations.

From the 1st equation, we get,

x = 14 â€“ y

Now, substitute the value of x to the second equation to get,

(14 â€“ y) â€“ y = 4

14 â€“ 2y = 4

2y = 10

Or y = 5

By the value of y, we can now find the exact value of x.

âˆµ x = 14 â€“ y

âˆ´ x = 14 â€“ 5

Or x = 9

Hence, x = 9 and y = 5

(ii) Given,

s â€“ t = 3 and (s/3) + (t/2) = 6 are the two equations.

From the 1st equation, we get,

s = 3 + t ________________(1)

Now, substitute the value of s to the second equation to get,

(3+t)/3 + (t/2) = 6

â‡’ (2(3+t) + 3t )/6 = 6

â‡’ (6+2t+3t)/6 = 6

â‡’ (6+5t) = 36

â‡’5t = 30

â‡’t = 6

Now, substitute the value of t to the equation (1)

s = 3 + 6 = 9

Therefore, s = 9 and t = 6

(iii) Given,

3x â€“ y = 3 and 9x â€“ 3y = 9 are the two equations.

From the 1st equation, we get,

x = (3+y)/3

Now, substitute the value of x to the second equation to get,

9(3+y)/3 â€“ 3y = 9

â‡’9 +3y -3y = 9

â‡’ 9 = 9

Therefore, y has infinite values, and since x = (3+y) /3, x also has infinite values.

(iv) Given,

0.2x + 0.3y = 1.3 and 0.4x + 0.5y = 2.3 are the two equations.

From the 1st equation, we get,

x = (1.3- 0.3y)/0.2 _________________(1)

Now, substitute the value of x to the second equation to get,

0.4(1.3-0.3y)/0.2 + 0.5y = 2.3

â‡’2(1.3 â€“ 0.3y) + 0.5y = 2.3

â‡’ 2.6 â€“ 0.6y + 0.5y = 2.3

â‡’ 2.6 â€“ 0.1 y = 2.3

â‡’ 0.1 y = 0.3

â‡’ y = 3

Now, substitute the value of y in equation (1), and we get,

x = (1.3-0.3(3))/0.2 = (1.3-0.9)/0.2 = 0.4/0.2 = 2

Therefore, x = 2 and y = 3

(v) Given,

âˆš2 x + âˆš3 y = 0 and âˆš3 x â€“ âˆš8 y = 0

are the two equations.

From the 1st equation, we get,

x = â€“ (âˆš3/âˆš2)y __________________(1)

Putting the value of x in the given second equation to get,

âˆš3(-âˆš3/âˆš2)y â€“ âˆš8y = 0 â‡’ (-3/âˆš2)y- âˆš8 y = 0

â‡’ y = 0

Now, substitute the value of y in equation (1), and we get,

x = 0

Therefore, x = 0 and y = 0

(vi) Given,

(3x/2)-(5y/3) = -2 and (x/3) + (y/2) = 13/6 are the two equations.

From 1st equation, we get,

(3/2)x = -2 + (5y/3)

â‡’ x = 2(-6+5y)/9 = (-12+10y)/9 â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦(1)

Putting the value of x in the second equation, we get,

((-12+10y)/9)/3 + y/2 = 13/6

â‡’y/2 = 13/6 â€“( (-12+10y)/27 ) + y/2 = 13/6

Now, substitute the value of y in equation (1), and we get,

(3x/2) â€“ 5(3)/3 = -2

â‡’ (3x/2) â€“ 5 = -2

â‡’ x = 2

Therefore, x = 2 and y = 3

2. Solve 2x + 3y = 11 and 2x â€“ 4y = â€“ 24 and hence find the value of â€˜mâ€™ for which y = mx + 3.

Solution:

2x + 3y = 11â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦..(I)

2x â€“ 4y = -24â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦ (II)

From equation (II), we get

x = (11-3y)/2 â€¦â€¦â€¦â€¦â€¦â€¦â€¦.(III)

Substituting the value of x to equation (II), we get

2(11-3y)/2 â€“ 4y = 24

11 â€“ 3y â€“ 4y = -24

-7y = -35

y = 5â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦..(IV)

Putting the value of y in equation (III), we get

x = (11-3Ã—5)/2 = -4/2 = -2

Hence, x = -2, y = 5

Also,

y = mx + 3

5 = -2m +3

-2m = 2

m = -1

Therefore, the value of m is -1.

3. Form the pair of linear equations for the following problems and find their solution by the substitution method.

(i) The difference between two numbers is 26, and one number is three times the other. Find them.

Solution:

Let the two numbers be x and y, respectively, such that y > x.

According to the question,

y = 3x â€¦â€¦â€¦â€¦â€¦â€¦ (1)

y â€“ x = 26 â€¦â€¦â€¦â€¦..(2)

Substituting the value of (1) to (2), we get

3x â€“ x = 26

x = 13 â€¦â€¦â€¦â€¦â€¦. (3)

Substituting (3) in (1), we get y = 39

Hence, the numbers are 13 and 39.

(ii) The larger of two supplementary angles exceeds, the smaller by 18 degrees. Find them.

Solution:

Let the larger angle be xo and the smaller angle be yo.

We know that the sum of two supplementary pairs of angles is always 180o.

According to the question,

x + y = 180oâ€¦â€¦â€¦â€¦â€¦. (1)

x â€“ y = 18oÂ â€¦â€¦â€¦â€¦â€¦..(2)

From (1), we get x = 180oÂ â€“ y â€¦â€¦â€¦â€¦. (3)

Substituting (3) in (2), we get

180oÂ â€“ y â€“ y =18o

162oÂ = 2y

y = 81oÂ â€¦â€¦â€¦â€¦.. (4)

Using the value of y in (3), we get

x = 180oÂ â€“ 81o

= 99o

Hence, the angles are 99oÂ and 81o.

(iii) The coach of a cricket team buys 7 bats and 6 balls for Rs.3800. Later, she buys 3 bats and 5 balls for Rs.1750. Find the cost of each bat and each ball.

Solution:

Let the cost of a bat be x and the cost of a ball be y.

According to the question,

7x + 6y = 3800 â€¦â€¦â€¦â€¦â€¦â€¦. (I)

3x + 5y = 1750 â€¦â€¦â€¦â€¦â€¦â€¦. (II)

From (I), we get

y = (3800-7x)/6â€¦â€¦â€¦â€¦â€¦â€¦..(III)

Substituting (III) to (II), we get,

3x+5(3800-7x)/6 =1750

â‡’3x+ 9500/3 â€“ 35x/6 = 1750

â‡’3x- 35x/6 = 1750 â€“ 9500/3

â‡’(18x-35x)/6 = (5250 â€“ 9500)/3

â‡’-17x/6 = -4250/3

â‡’-17x = -8500

x = 500 â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦.. (IV)

Substituting the value of x to (III), we get

y = (3800-7 Ã—500)/6 = 300/6 = 50

Hence, the cost of a bat is Rs 500, and the cost of a ball is Rs 50.

(iv) The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of 10 km, the charge paid is Rs 105 and for a journey of 15 km, the charge paid is Rs 155. What are the fixed charges and the charge per km? How much does a person have to pay for travelling a distance of 25 km?

Solution:

Let the fixed charge be Rs x and the per km charge be Rs y.

According to the question,

x + 10y = 105 â€¦â€¦â€¦â€¦â€¦.. (1)

x + 15y = 155 â€¦â€¦â€¦â€¦â€¦.. (2)

From (1), we get x = 105 â€“ 10y â€¦â€¦â€¦â€¦â€¦â€¦. (3)

Substituting the value of x to (2), we get

105 â€“ 10y + 15y = 155

5y = 50

y = 10 â€¦â€¦â€¦â€¦â€¦.. (4)

Putting the value of y in (3), we get

x = 105 â€“ 10 Ã— 10 = 5

Hence, the fixed charge is Rs 5 and the per km charge = Rs 10

Charge for 25 km = x + 25y = 5 + 250 = Rs 255

(v) A fraction becomes 9/11 if 2 is added to both the numerator and the denominator. If 3 is added to both the numerator and the denominator, it becomes 5/6. Find the fraction.

Solution:

Let the fraction be x/y.

According to the question,

(x+2) /(y+2) = 9/11

11x + 22 = 9y + 18

11x â€“ 9y = -4 â€¦â€¦â€¦â€¦â€¦.. (1)

(x+3) /(y+3) = 5/6

6x + 18 = 5y +15

6x â€“ 5y = -3 â€¦â€¦â€¦â€¦â€¦â€¦. (2)

From (1), we get x = (-4+9y)/11Â â€¦â€¦â€¦â€¦â€¦.. (3)

Substituting the value of x to (2), we get

6(-4+9y)/11 -5y = -3

-24 + 54y â€“ 55y = -33

-y = -9

y = 9 â€¦â€¦â€¦â€¦â€¦â€¦â€¦ (4)

Substituting the value of y to (3), we get

x = (-4+9Ã—9 )/11 = 7

Hence, the fraction is 7/9.

(vi) Five years hence, the age of Jacob will be three times that of his son. Five years ago, Jacobâ€™s age was seven times that of his son. What are their present ages?

Solutions:

Let the age of Jacob and his son be x and y, respectively.

According to the question,

(x + 5) = 3(y + 5)

x â€“ 3y = 10 â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦.. (1)

(x â€“ 5) = 7(y â€“ 5)

x â€“ 7y = -30 â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦. (2)

From (1), we get x = 3y + 10 â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦. (3)

Substituting the value of x to (2), we get

3y + 10 â€“ 7y = -30

-4y = -40

y = 10 â€¦â€¦â€¦â€¦â€¦â€¦â€¦ (4)

Substituting the value of y to (3), we get

x = 3 x 10 + 10 = 40

Hence, the present age of Jacob and his son is 40 years and 10 years, respectively.

Exercise 3.3 contains a total of 3 questions. The solutions to these questions are provided in the NCERT Solutions for Class 10 Maths Chapter 3 â€“ Pair of Linear Equations in Two Variables Exercise 3.3. The students can refer to this page for the answers. The solutions with accurate steps are provided in the NCERT Solutions. The students will find it helpful in case of any doubts.

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