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

**NCERT Solutions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables **are discussed here. Class 10 Maths chapter 3 is an important chapter of Algebra and this chapter are created by expert team at careers360 keeping in mind of latest CBSE syllabus 2023. In Class 10 Maths chapter 3 solutions, students will learn to solve the linear equation with two variables. Class 10 Maths chapter 3 NCERT solutions contain the answers of all exercise NCERT questions.

NCERT Solutions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables NCERT Class 10 Maths chapter 3 solutions are helpful to know the answers to the questions asked in NCERT class 10 maths book. Apart from this, by going through NCERT solutions for class 10 maths chapter 3, they will come to know about various methods of solving questions. NCERT solutions for class 10 are also available for other subjects.

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## Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables PDF Free Download

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## Pair of Linear Equations in Two Variables Class 10- Important Formulae

Types of Linear Equations:

S. No. | Types of Linear Equation | General form | Description | Solutions |

1. | Linear Equation in one Variable | ax + b = 0 | Where a ≠ 0 and a & b are real numbers | One Solution |

2. | Linear Equation in Two Variables | ax + by + c = 0 | Where a ≠ 0 & b ≠ 0 and a, b & c are real numbers | Infinite Solutions possible |

3. | Linear Equation in Three Variables | ax + by + cz + d = 0 | Where a ≠ 0, b ≠ 0, c ≠ 0 and a, b, c, d are real numbers | Infinite Solutions possible |

Simultaneous System of Linear Equations: A pair of equations in the format:

a_{1}x + b_{1}y + c_{1} = 0

a_{2}x + b_{2}y + c_{2} = 0

This arrangement is visually depicted through the use of two straight lines on the Cartesian plane, as explained in the following context:

When there is a unique solution then

x/(b_{1}c_{2} - b_{2}c_{1}) = y/(c_{1}a_{2} - c_{2}a_{1}) = 1/(a_{1}b_{2} - a_{2}b_{2})

This formula can be remembered as the diagram given below

Free download **NCERT Solutions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables PDF **for CBSE Exam.

## NCERT Solutions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables (Intext Questions and Exercise)

** Class 10 Maths Chapter 3 solutions Pair of Linear Equations in two variables Excercise: 3.1**

Q1 Aftab tells his daughter, “Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be.” (Isn’t this interesting?) Represent this situation algebraically and graphically.

Answer: Let x be the age of Aftab and y be the age of his daughter

Now, According to the question,

Also,

Now, let's represent both equations graphically,

From (1), we get

So, Putting different values of x we get corresponding values of y

And From (2) we get,

So, Putting different values of x we get corresponding values of y

GRAPH:

Q3 The cost of 2 kg of apples and 1kg of grapes on a day was found to be Rs 160. After a month, the cost of 4 kg of apples and 2 kg of grapes is Rs 300. Represent the situation algebraically and geometrically.

Answer:

Let, x be the cost of 1kg apple and y be the cost of 1kg grapes.

Now, According to the question,

On a day:

After One Month:

Now, From (1) we have

Putting different values of x we get corresponding values of y, so,'

And From (2) we have,

Putting different values of x we get corresponding values of y, so,

Graph:

**Class 10 Maths Chapter 3 solutions Pair of Linear Equations in Two Variables Excercise: 3.2**

Q1 Form the pair of linear equations in the following problems and find their solutions graphically.

(i) 10 students of Class X took part in a Mathematics quiz. If the number of girls is 4 more than the number of boys, find the number of boys and girls who took part in the quiz.

Answer:

Let the number of boys is x and the number of girls is y.

Now, According to the question,

Total number of students in the class = 10, i.e.

And

the number of girls is 4 more than the number of boys,i.e.

Different points (x, y) for equation (1)

Different points (x,y) satisfying (2)

Graph,

As we can see from the graph, both lines intersect at the point (7,3). that is x= 7 and y = 3 which means the number of boys in the class is 7 and the number of girls in the class is 3.

Q1 Form the pair of linear equations in the following problems and find their solutions graphically.

(ii) 5 pencils and 7 pens together cost Rs 50, whereas 7 pencils and 5 pens together cost Rs 46. Find the cost of one pencil and that of one pen.

Answer:

Let x be the price of 1 pencil and y be the price of 1 pen,

Now, According to the question

And

Now, the points (x,y), that satisfies the equation (1) are

And, the points(x,y) that satisfies the equation (2) are

The Graph,

As we can see from the Graph, both line intersects at point (3,5) that is, x = 3 and y = 5 which means cost of 1 pencil is 3 and the cost of 1 pen is 5.

Q7 Draw the graphs of the equations and . Determine the coordinates of the vertices of the triangle formed by these lines and the x-axis, and shade the triangular region.

### Answer:

Given, two equations,

And

The points (x,y) satisfying (1) are

And The points(x,y) satisfying (2) are,

GRAPH:

As we can see from the graph that both lines intersect at the point (2,3), And the vertices of the Triangle are ( -1,0), (2,3) and (4,0). The area of the triangle is shaded with a green color.

**Pair of linear equations in two variables class 10 solutions**** Excercise: 3.3**

Q1 Solve the following pair of linear equations by the substitution method. (i)

Answer:

Given, two equations,

Now, from (1), we have

Substituting this in (2), we get

Substituting this value of x in (3)

Hence, Solution of the given equations is x = 9 and y = 5.

Q1 Solve the following pair of linear equations by the substitution method (ii)

Answer:

Given, two equations,

Now, from (1), we have

Substituting this in (2), we get

Substituting this value of t in (3)

Hence, Solution of the given equations is s = 9 and t = 6.

**Pair of linear equations in two variables class 10 solutions**** Excercise: 3.4**

Q1 Solve the following pair of linear equations by the elimination method and the substitution method :

(i)

Answer:

Elimination Method:

Given, equations

Now, multiplying (1) by 3 we, get

Now, Adding (2) and (3), we get

Substituting this value in (1) we, get

Hence,

Substitution method :

Given, equations

Now, from (1) we have,

substituting this value in (2)

Substituting this value of x in (3)

Hence,

Q1 Solve the following pair of linear equations by the elimination method and the substitution method :

(ii)

Answer:

Elimination Method:

Given, equations

Now, multiplying (2) by 2 we, get

Now, Adding (1) and (3), we get

Putting this value in (2) we, get

Hence,

Substitution method :

Given, equations

Now, from (2) we have,

substituting this value in (1)

Substituting this value of x in (3)

Hence,

Q1 Solve the following pair of linear equations by the elimination method and the substitution method: (iii)

Answer:

Elimination Method:

Given, equations

Now, multiplying (1) by 3 we, get

Now, Subtracting (3) from (2), we get

Putting this value in (1) we, get

Hence,

Substitution method :

Given, equations

Now, from (2) we have,

substituting this value in (1)

Substituting this value of x in (3)

Hence,

Q1 Solve the following pair of linear equations by the elimination method and the substitution method :(iv)

Answer:

Elimination Method:

Given, equations

Now, multiplying (2) by 2 we, get

Now, Adding (1) and (3), we get

Putting this value in (2) we, get

Hence,

Substitution method :

Given, equations

Now, from (2) we have,

substituting this value in (1)

Substituting this value of x in (3)

Hence,

Q1 Solve the following pairs of equations by reducing them to a pair of linear equations:

(viii)

### Answer:

Given Equations,

Let,

Now, our equation becomes

And

Now, Adding (1) and (2), we get

Putting this value in (1)

Now,

And

Now, Adding (3) and (4), we get

Putting this value in (3),

Hence,

Q2 Formulate the following problems as a pair of equations and hence find their solutions: (i) Ritu can row downstream 20 km in 2 hours, and upstream 4 km in 2 hours. Find her speed of rowing in still water and the speed of the current.

### Answer:

Let the speed of Ritu in still water be x and speed of current be y,

Let's solve this problem by using relative motion concept,

the relative speed when they are going in the same direction (downstream)= x +y

the relative speed when they are going in the opposite direction (upstream)= x - y

Now, As we know,

Relative distance = Relative speed * time .

So, According to the question,

And,

Now, Adding (1) and (2), we get

Putting this in (2)

Hence,

Hence Speed of Ritu in still water is 6 km/hour and speed of the current is 4 km/hour

Q2 Formulate the following problems as a pair of equations and hence find their solutions: (ii) 2 women and 5 men can together finish an embroidery work in 4 days, while 3 women and 6 men can finish it in 3 days. Find the time taken by 1 woman alone to finish the work, and also that taken by 1 man alone.

### Answer:

Let the number of days taken by woman and man be x and y respectively,

The proportion of Work done by a woman in a single day

The proportion of Work done by a man in a single day

Now, According to the question,

Also,

Let,

Now, our equation becomes

And

By Cross Multiplication method,

So,

Q3 A train covered a certain distance at a uniform speed. If the train would have been 10 km/h faster, it would have taken 2 hours less than the scheduled time. And, if the train were slower by 10 km/h; it would have taken 3 hours more than the scheduled time. Find the distance covered by the train.

Answer:

Let the speed of the train be v km/h and the time taken by train to travel the given distance be t hours and the distance to travel be d km.

Now As we Know,

Now, According to the question,

Now, Using equation (1), we have

Also,

Adding equations (2) and (3), we obtain:

Substituting the value of x in equation (2), we obtain:

Putting this value in (1) we get,

Hence the distance covered by train is 600km.

Q5 In a , . Find the three angles.

Answer:

Given,

Also, As we know that the sum of angles of a triangle is 180, so

Now From (1) we have

Putting this value in (2) we have

Putting this in (3)

And

Hence three angles of triangles

Q7 Solve the following pair of linear equations: (v)

Answer:

Given Equations,

As we can see by adding and subtracting both equations we can make our equations simple to solve.

So,

Adding (1) and )2) we get,

Subtracting (2) from (1) we get,

Now, Adding (3) and (4) we get,

Putting this value in (3)

Hence,

### Class 10 Maths Chapter 3 Topics

Solving a linear equation with two variables.

Representation of linear equation in a graph.

Solutions of linear equations using the graph.

Algebraic interpretation of linear equations.

Formation of linear equations using statements.

**Also get the solutions exercise wise-**

## Key Features of NCERT Class 10 Maths Solutions Chapter 3

- The questions and their answers given in Chapter 3 Class 10 Maths NCERT solutions are very interesting and important for board and competitive exams.
- NCERT solutions for Maths chapter 3
**Linear Equations in Two Variables Class 10** will help to boost preparation for all of the examinations. Many real-life situations can be formulated using Mathematical equations given in this chapter 3 NCERT Class 10 Maths solutions.

For example, consider the statement "cost of 1 Kg Apple and 2Kg orange is 120 and the cost of 3 Kg Apple and 1 Kg orange is 210". The statement can be formulated using the Mathematical equation, for this consider the cost of Apple as x and that of orange as y. Then we can write two equations as x+2y=120 and 3x+y=210.

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### How to use NCERT Solutions for Class 10 Maths Chapter 3?

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NCERT solutions Class 10 Maths Chapter 3 are the most important tool when you are appearing for board examinations. 90% paper of CBSE board examinations, directly come from the NCERT.

Now you have done the NCERT solutions for Class 10 Maths chapter 3 and learned the approach to solving questions in the step by step method.

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