NCERT Solutions for Pair of Linear Equations in Two Variables Exercise 3.3 Class 10 Maths

Exercise 3.3 Class 10 Maths: An equation is said to be a linear equation in two variables when, in an equation ax+by+c, where a,b and c are real numbers and not equal to zero. On the other hand, a pair of linear equation in two variables is the equation with two such linear equations. The final answer of such an equation is shown as a point on the line representing the equation. Students will be studying how to derive an equation and represent it on a line in NCERT Solutions for Pair of Linear equations in two variables exercise 3.3 Class 10 Maths.

Students who solve the NCERT Solutions Exercise 3.3 Class 10 Maths can easily learn the Substitution Method and solve the relevant questions easily. The exercise 3.3 Class 10 Maths has three practice questions which are sufficient for students to grasp the concept covered therein. In this article, we have provided the NCERT Solutions for Exercise 3.3 Class 10 Maths pdf.

NCERT Solutions for Pair of Linear Equations in Two Variables Exercise 3.3 Class 10 Maths: Overview

The NCERT Solutions for Pair of Linear Equations in Two Variables Exercise 3.3 Class 10 Maths deals with the topic Substitution Method. In this method, students have to find the value of one variable in terms of another variable from either of the equations, whichever is convenient to them.

Then, the value of one variable is substituted in another equation, the new equation thus derived is then reduced to an equation with one variable which can then be simplified. Sometimes there can be a statement with no variable.

In case the statement is true, students can conclude that the pair of linear equations have infinite solutions. If the statement is false, then the pair of linear equations is inconsistent.  Another way of implementing the substitution method is by substituting the value of wither x or y variable in the equation and then equate the two equations to find the solution.

Exercise 3.3 Class 10 Maths can be easily solved by relating two equations and finding a common variable between them. Before we go into the chapter summary section, check the overview of the NCERT Solutions Exercise 3.3 Class 10 Maths Chapter 3 here:

NCERT Solutions for Pair of Linear Equations in Two Variables Exercise 3.3 Class 10 Maths PDF

It can be highly beneficial is students solve the topic-wise intext questions and miscellaneous exercises from Embibe’s NCERT Class 10 Maths Solutions Chapter 3. Also, there are exercise 3.3 Class 10 Maths questions to help students practice and strengthen their conceptual understanding of the topic. Solving problems will help students memorise the formulas and implement them correctly in the question.

NCERT Solutions for Pair of Linear Equations in Two Variables Exercise 3.3 Class 10 Maths: About the Exercise

In the NCERT Solutions for Pair of Linear Equations in two variables Exercise 3.3 Class 10 Maths, students will learn the Substitution Method. It is the first part of the topic Algebraic Methods of Solving a Pair of Linear Equations. In this exercise, there are three questions requiring students to implement the substitution method in different ways.

In the first two questions, students are required to solve pairs of linear equations by the substitution method, solve the given equations and find the value of a variable. The third question tests the depth of students’ understanding of the concept. Here, one has to first form the pair of linear equations and solve different problems based on the equations.

The three sub-questions to be solved are difference is given between two numbers and one number is three times the other, and students have to both the numbers. (ii) The greater of two supplementary angles exceeds the smaller by certain degrees and students have to find both the angles. (iii) The coach of a cricket team buys x number of bats and y number of balls for z amount. She then buys bats and b balls for c amount. Students have to find the cost of each bat and each ball.

NCERT Solutions for Pair of Linear Equations in Two Variables Exercise 3.3 Class 10 Maths: Chapter Summary

In the NCERT Class 10 Maths Chapter 2 Pair of Linear Equations in Two Variables, students will learn the following concepts:

• Two linear equations in the same two variables are called a pair of linear equations in two variables. The most general form of a pair of linear equations is a1 x + b1 y + c1 = 0 a2 x + b2 y + c2 = 0, Where, a1, b1, c1, a2, b2, c2 are real number and are not equal to zero.

• A pair of linear equations in two variables can be represented, and solved, by the: (i) graphical method (ii) algebraic method 
• Graphical Method: The graphical representation of a pair of linear equations in two variables is done with two lines. 

(i) If both the lines intersect at a certain point, then that common point provides the solution to the two equations. In such a case, the pair of equations is said to be consistent.
(ii) If the lines coincide at any point, then there can be infinite solutions, with each point on the line being a possible solution. In such a case, the pair of equations is dependent or consistent.
(iii) If both the lines are parallel to each other, then the pair of equations can have solution. In such a scenario, the pair of equations is inconsistent.

• Algebraic Methods: The solution of a pair of linear equations can be found using the following three methods
  (i) Substitution Method (ii) Elimination Method (iii) Cross-multiplication Method
• There are many situations which can be mathematically represented with the help of two equations, that are not linear initially but can be altered and reduced to a pair of linear equations.

Advantages of Studying From NCERT Solutions for Pair of Linear Equations in Two Variables Exercise 3.3 Class 10 Maths

There are several benefits of practising Embibe’s exercise 3.3 Class 10 Maths NCERT Solutions, which are listed below:

• Embibe’s subject specialists have curated these NCERT Solutions exercise 3.3 Class 10 Maths.
• The answers are provided in step-wise approach and students can cross-check their own performance against the answers provided in the exercise 3.3 Class 10 Maths NCERT solutions.
• The Exercise 3.3 Class 10 Maths NCERT solutions provide make understanding the topic easily. This enables students to implement the concepts in different types of questions correctly.
• By referring to the NCERT Solutions for linear equations Class 10 exercise 3.3 students can learn how to substitute the variables between two equations and find values for both the variables. 

Students can download the exercise 3.3 Class 10 Maths pdf offline and practice the questions at their convenience.

NCERT Solutions for Pair of Linear Equations in Two Variables Exercise 3.3 Class 10 Maths: All Chapters PDF

Students can download the NCERT Solutions Class 10 Maths pdf for all chapters from the table below:

FAQs on Pair of Linear Equations in Two Variables Exercise 3.3 Class 10 Maths

Here are some of the most frequently asked questions on NCERT Solutions for Pair of Linear Equations in Two Variables Ex 3.3 Class 10 Maths:

Q.1: Where can I get the exercise 3.3 Class 10 Maths NCERT Solutions PDF?
Ans: Students can download the exercise 3.3 Class 10 Maths NCERT Solutions pdf format for in this article. It can also be downloaded from the NCERT official website with the link given above or Embibe.com.

Q.2: Are NCERT Solutions Class 10 Maths sufficient for board exam preparation?
Ans: The NCERT textbooks and NCERT Solutions are the books prescribed for Class 10. These books are sufficient for the Class 10 board exam. 

Q.3: Where can I learn the concepts of Pair of Linear Equations in Two Variables Exercise 3.3?
Ans: Students can learn and practice the topic Substitution Method by solving the questions given in exercise 3.3 Class 10 Maths NCERT Solutions. 

Q.4: What are the concepts covered in the NCERT Solutions for Class 10 Maths Chapter 3?
Ans: The NCERT Solutions Class 10 Maths Chapter 3 covers the topics graphical and algebraic representation of solving a pair of linear equations, cross multiple method, Equations Reducible to a Pair of Linear Equations in Two Variables. 

Q.5: How many exercises are there in NCERT Solutions for Pair of Linear Equations in Two Variables Class 10 Maths Chapter 3?
Ans: There are seven exercises in the NCERT Solutions for Pair of Linear Equations in Two Variables Class 10 Maths Chapter 3. 

After a topic is taught in the classroom, students should practice the intext exercises to strengthen their understanding of the concept. It will help them solve problems correctly in the final exam. The NCERT Solutions for Pair of Linear Equations in Two Variables Exercise 3.3 Class 10 Maths will clear students’ doubts as it contains questions requiring different application of the same concept.

Students can check Embibe’s 3D interactive videos, sample papers and take mock tests for all the CBSE Class 10 subjects and do a comprehensive board exam preparation. 

We hope this article on NCERT Solutions for Pair of Linear Equations in Two Variables Exercise 3.3 Class 10 Maths was helpful to you.

Stay tuned to Embibe for more all the latest updates on CBSE Class 10 Maths, preparation tips, exam dates, results and the latest academic events!