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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 the best study guide to master the concepts of this chapter. With these solutions, you can prepare well for your Class 10 Maths board exam. The solutions are created in a stepwise manner by askIITians elite Maths faculty. These NCERT Solutions include easy to understand explanations for every question so that you are well-versed with how to approach questions related to Linear Equations in Two Variables. Let us see what has been included in these NCERT Class 10 Maths Solutions for you. 

 

About NCERT Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables

 

Pair of Linear Equations in Two Variables is one of the longest chapters of Class 10 Maths with 7 exercises. This chapter includes topics like solving pairs of linear equations in two variables using the graphical method, substitution method, elimination method, and cross-multiplication method and reducing equations to a pair of linear equations in two variables. 

 

Important points to take note of while solving the NCERT Solutions for Pair of Linear Equations in Two Variables: 

 

Linear Equation with Two Variables: An equation which can be put in the form: ax + by + c = 0, where a, b and c are real numbers (a, b ≠ 0) is called a linear equation in two variables ‘x’ and ‘y’. 

 

Pair of Linear Equation with Two Variables: General form of a linear pair of equations in two variables is: a1x + b1y + c1 - 0 and a2x + b2y + c2 = 0

where a1 b1, c1, a2, b2, c2 are real numbers. 

 

Solution of Pair of Linear Equations in Two Variables: Pair of linear equations can be solved using two methods: 

  1. Graphical Method 
  2. Algebraic Method 

In the graphical method, we observe the graphs of the two equations based on the following: 

  1. If the graphs of two equations of a system intersect at a point, the system is said to have a unique solution. In other words, the pair of linear equations is consistent.
  2. If the graphs of two equations of a system are two parallel lines, the system is said to have no solution. In other words, the pair of linear equations is inconsistent.
  3. When the graphs of two equations of a system are two coincident lines, the system is said to have infinitely many solutions. In other words, the pair of linear equations is consistent and dependent.

The algebraic method of solving a pair of linear equations includes three methods: 

  1. Substitution 
  2. Elimination 
  3. Cross-multiplication 

The solutions of a pair of linear equations in two variables depend upon: 

  1. If a1/a2 ≠ b1/b2, then the pair of linear equations is consistent,
  2. If a1/a2 = b1/b2, then the pair of linear equations is inconsistent,
  3. If a1/a2 = b1/b2 = c1/c2, then the pair of linear equations is consistent and dependent. 

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

 

The exercise questions in NCERT Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables include: 

  • representing the given situations graphically, 
  • finding whether the given pair of linear equations intersect at a point, parallel or coincident, and 
  • finding the solutions of the given linear equations using different methods. 

NCERT Solutions for Class 10 Maths Chapter 3 Ex 3.1 

 

The first exercise of this chapter is an introductory exercise about the pair of linear equations in two variables. It includes only 3 questions where you are given three different word problems. You have to read them, interpret them and create linear equations. You also have to represent them graphically. 

 

NCERT Solutions for Class 10 Maths Chapter 3 Ex 3.2 

 

The second exercise of Pair of Linear Equations in Two Variables is based on solving a pair of linear equations using the graphical method. The exercise includes 7 questions whose stepwise solutions are provided in our NCERT Solutions for Class 10 Maths. Read them carefully to master the concept of this exercise. 

 

NCERT Solutions for Class 10 Maths Chapter 3 Ex 3.3

 

The third exercise of chapter 3 is based on solving a pair of linear equations using the substitution method. The exercise includes only 3 questions. But the third question 6 parts where you are given different situations. You have to form a pair of linear equations for each and find their solution using the substitution method. 

 

NCERT Solutions for Class 10 Maths Chapter 3 Ex 3.4 

 

The fourth exercise of the chapter is based on solving a pair of linear equations using the elimination method. The exercise includes only 2 questions. But the second question includes 5 parts where you are given 5 different word problems. You have to read them, formulate the linear equations and find their solution using the elimination method. Check our NCERT Solutions for stepwise answers to this exercise. 

 

NCERT Solutions for Class 10 Maths Chapter 3 Ex 3.5

 

The fifth exercise of the chapter is based on solving a pair of linear equations using the cross-multiplication method. This exercise includes 4 questions out of which the last question is the toughest of all. Just like the above two exercises, this question also includes different word problems where formulate the linear equations and find their solution using the cross-multiplication method. 

 

NCERT Solutions for Class 10 Maths Chapter 3 Ex 3.6 

 

The sixth exercise of Pair of Linear Equations with Two Variables is based on reducing equations to a pair of linear equations in two variables. There are 2 questions in this exercise. The first question has 8 subparts where we have to solve the given pairs of equations by reducing them to a pair of linear equations. The second question includes 3 subparts where you have to read and interpret the word problems, formulate the pair of linear equations and solve them. 

 

NCERT Solutions for Class 10 Maths Chapter 3 Ex 3.7

 

The last exercise of the chapter is an optional exercise with 8 questions. This means that questions given in this exercise are not from the point of view of the exam. However, we recommend you solve this exercise to test your knowledge. In case you face any problems, our NCERT online Solutions are available for you. 

 

Download free exercise-wise solutions for Class 10 Maths Pair of Linear Equations in Two Variables:

 

  • NCERT Chapter 3 Class 10 Maths Ex 3.1 Solutions 
  • NCERT Chapter 3 Class 10 Maths Ex 3.2 Solutions
  • NCERT Chapter 3 Class 10 Maths Ex 3.3 Solutions 
  • NCERT Chapter 3 Class 10 Maths Ex 3.4 Solutions
  • NCERT Chapter 3 Class 10 Maths Ex 3.5 Solutions 
  • NCERT Chapter 3 Class 10 Maths Ex 3.6 Solutions 
  • NCERT Chapter 3 Class 10 Maths Ex 3.7 Solutions 

NCERT Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables FAQs

 

1. What are the main topics of Chapter 3 Pair of Linear Equations in Two Variables Class 10 Maths? 

 

The main topics included in Chapter 3 Pair of Linear Equations in Two Variables are solving pairs of linear equations in two variables using the graphical method, substitution method, elimination method, and cross-multiplication method and reducing equations to a pair of linear equations in two variables. 

 

2. How many questions are there in NCERT Class 10 Maths Chapter 3? 

 

Pair of Linear Equations in Two Variables Chapter 3 of Class 10 Maths includes 32 questions and 7 unsolved exercises. 

 

3. How to prepare NCERT Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables? 

 

Download free revision notes and NCERT Solutions from the askIITians website. We also provide one-on-one and batch-wise online classes for grade 10 students where our experts teach you in live, interactive sessions. 


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