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NCERT Solutions for Class 10 Maths Chapter 3: Pair of Linear Equations in Two Variables are provided in this article. A pair of linear equations in two variables having a solution is known as a consistent pair of linear equations. Equivalent pair of linear equations has infinitely many distinct common solutions, such a pair of solutions is known as a dependent pair of linear equations in two variables.

Class 10 Maths Chapter 3 Linear Equations in Two Variables belongs to Unit 2 Algebra which has a weightage of 20 marks in the CBSE Class 10 Maths Examination. The NCERT solutions of the chapter include questions related to the Substitution method, Elimination method, and Cross-multiplication method.

Download PDF: NCERT Solutions for Class 10 Mathematics Chapter 3

NCERT Solutions for Class 10 Mathematics Chapter 3

NCERT Solutions

Important Topics in Class 10 Maths Chapter 3

Linear Equations are the equations in which the powers of all the involved variables are one.

The general form of a linear equation in two variables is ax + by + c = 0, where a and b cannot be simultaneously zero.

The solution of a linear equation in two variables is generally a pair of values, one for x and the other for y, which makes the two sides of the equation equal.

For example: If 3x + y = 6, then (0,6) is one of its solutions as it satisfies the equation.

Graph of Linear Equation in two variables: A linear equation in two variables can be geometrically represented as a straight line.

A pair of linear equations in two variables can be represented as shown below –

\(a_1x + b_1y+c_1=0\\ a_2x + b_2y+c_2=0\)

The solution for a consistent pair of linear equations can be found using various methods.

i) Elimination method

ii) Substitution Method

iii) Cross-multiplication of solving linear equations

iv) Graphical method

NCERT Solutions For Class 10 Maths Chapter 3 Exercises:

The detailed solutions for all the NCERT Solutions for Pair of Linear Equations in Two Variables under different exercises are as follows:

Related Topics:

Difference between linear and non-linear equations	Pair of Linear Equations in Two Variables Important Questions	Pair of Linear Equations in Two Variables Formula

CBSE Class 10 Mathematics Study Guides:

Geometry	Math Formula	Maths Study Material
NCERT Solutions for Class 10 Maths	Class 10 Maths Notes	Mensuration
Difference between in Maths	Calculus	Math MCQs

CBSE X Related Questions

1.
If 3 cot A = 4, check whether \(\frac{(1-\text{tan}^2 A)}{(1+\text{tan}^2 A)}\) = cos² A – sin²A or not

View Solution

2.
The lengths of 40 leaves of a plant are measured correct to the nearest millimetre, and the data obtained is represented in the following table :
Length (in mm)
Number of leaves
118 - 126
3
127 - 135
5
136 - 144
9
145 - 153
12
154 - 162
5
163 - 171
4
172 - 180
2
Find the median length of the leaves.
(Hint : The data needs to be converted to continuous classes for finding the median, since the formula assumes continuous classes. The classes then change to 117.5 - 126.5, 126.5 - 135.5, . . ., 171.5 - 180.5.)

Length (in mm)	Number of leaves
118 - 126	3
127 - 135	5
136 - 144	9
145 - 153	12
154 - 162	5
163 - 171	4
172 - 180	2

View Solution

3.
Which of the following pairs of linear equations are consistent/inconsistent? If consistent, obtain the solution graphically: (i) \(x + y = 5\),\( 2x + 2y = 10\) (ii)\( x – y = 8 , 3x – 3y = 16\) (iii) \(2x + y – 6 = 0\) , \(4x – 2y – 4 = 0\) (iv) \(2x – 2y – 2 = 0,\) \( 4x – 4y – 5 = 0\)

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4.
The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the median, mean and mode of the data and compare them
Monthly consumption
(in units)
Number of consumers
65 - 85
4
85 - 105
5
105 - 125
13
125 - 145
20
145 - 165
14
165 - 185
8
185 - 205
4

Monthly consumption (in units)	Number of consumers
65 - 85	4
85 - 105	5
105 - 125	13
125 - 145	20
145 - 165	14
165 - 185	8
185 - 205	4

View Solution

5.
Solve the following pair of linear equations by the substitution method.
(i) x + y = 14
x – y = 4
(ii) s – t = 3
  \(\frac{s}{3} + \frac{t}{2}\) =6
(iii) 3x – y = 3
9x – 3y = 9
(iv) 0.2x + 0.3y = 1.3
0.4x + 0.5y = 2.3
(v)\(\sqrt2x\) + \(\sqrt3y\)=0
  \(\sqrt3x\) - \(\sqrt8y\) = 0
(vi) \(\frac{3x}{2} - \frac{5y}{3}\) =-2,
  \(\frac{ x}{3} + \frac{y}{2}\) = \(\frac{ 13}{6}\)

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6.
A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eyes to the top of the building increases from 30° to 60° as he walks towards the building. Find the distance he walked towards the building.

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NCERT Solutions for class 10 Maths Chapter 3: Pair Of Linear Equations In Two Variables

NCERT Solutions for Class 10 Mathematics Chapter 3

Important Topics in Class 10 Maths Chapter 3

NCERT Solutions For Class 10 Maths Chapter 3 Exercises:

CBSE X Related Questions

1.
If 3 cot A = 4, check whether \(\frac{(1-\text{tan}^2 A)}{(1+\text{tan}^2 A)}\) = cos² A – sin²A or not

6.
A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eyes to the top of the building increases from 30° to 60° as he walks towards the building. Find the distance he walked towards the building.

Similar Mathematics Concepts

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NCERT Solutions for class 10 Maths Chapter 3: Pair Of Linear Equations In Two Variables

NCERT Solutions for Class 10 Mathematics Chapter 3

Important Topics in Class 10 Maths Chapter 3

NCERT Solutions For Class 10 Maths Chapter 3 Exercises:

CBSE X Related Questions

1. If 3 cot A = 4, check whether \(\frac{(1-\text{tan}^2 A)}{(1+\text{tan}^2 A)}\) = cos2 A – sin2 A or not

4. The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the median, mean and mode of the data and compare themMonthly consumption (in units) Number of consumers65 - 85 485 - 1055105 - 12513125 - 14520145 - 16514165 - 1858185 - 2054

6. A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eyes to the top of the building increases from 30° to 60° as he walks towards the building. Find the distance he walked towards the building.

Similar Mathematics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
If 3 cot A = 4, check whether \(\frac{(1-\text{tan}^2 A)}{(1+\text{tan}^2 A)}\) = cos² A – sin²A or not

6.
A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eyes to the top of the building increases from 30° to 60° as he walks towards the building. Find the distance he walked towards the building.