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NCERT Solutions for Class 10 Maths Chapter 3: Pair of Linear Equations in Two Variables - Exercise 3.1

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

Practicing NCERT sums is a must if students wish to score well in the Class 10 examinations. The topics covered in Exercise 3.1 of NCERT Class 10th are very important as these are the fundamental concepts of linear equations. The Class 10 Maths Exercise 3.1 Solutions PDF is available for free download on Vedantu. These NCERT Solutions can be downloaded from the official website or the mobile app of Vedantu. Our subject experts prepared these NCERT class 10 maths chapter 3 exercise 3.1 so that students can refer to them and understand the problem-solving methods of linear equations. Students can also download NCERT Solutions for Class 10 Science for free on Vedantu.


Class:

NCERT Solutions for Class 10

Subject:

Class 10 Maths

Chapter Name:

Chapter 3 - Pair of Linear Equations in Two Variables

Exercise:

Exercise - 3.1

Content-Type:

Text, Videos, Images and PDF Format

Academic Year:

2023-24

Medium:

English and Hindi

Available Materials:

  • Chapter Wise

  • Exercise Wise

Other Materials

  • Important Questions

  • Revision Notes


Important Topics

  • Equation: An equation is a mathematical expression that states that two mathematical expressions with one or more variables are equal.

  • Linear Equation: A linear equation is an equation in which the maximum power of the variable of the equation is one. A linear equation's degree is always one.


What is the general form of a Linear Equation in Two Variables? 

A linear equation in two variables has the general form ax + by + c = 0, where a and b cannot be zero at the same time.


Representing Linear Equations for a Word Problem

To represent the word problems as linear equations,

  • Unknown quantities must be identified and denoted by variables.

  • Represent the relationships between quantities mathematically, using variables to replace the unknowns.


Solution of a Linear Equation in Two Variables

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


While plotting the Graph of a Linear Equation in Two Variables, please note that:

  • Every point whose coordinates satisfy the equation lies on the line.

  • Every point on the line gives a solution for x and y of the equation.

  • Any point, which will not lie on the line, is not a solution of the equation.

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

Exercise 3.1

1. 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.

Ans: Assuming that the present age of Aftab and his daughter are \[x\] and \[y\] respectively.

Seven years ago their age will be :

Aftab’s age: \[x-7\]

Aftab’s daughter age: \[y-7\]

Therefore, 

\[\left( x-7 \right)=7\left( y-7 \right)\]

\[x-7=7y-49\]

\[x-7y=-42\]                    …… (i)

Their age after three years:

Aftab’s age: \[x+3\]

Aftab’s daughter age: \[y+3\]

Therefore, 

\[\left( x+3 \right)=3\left( y+3 \right)\]

\[x+3=3y+9\]

\[x-3y=6\]                    …… (ii)

Representing equation (i) in algebraic form:

\[x=7y-42\]

Solution table:

\[x\]

\[-7\]

\[0\]

\[7\]

\[y\]

\[5\]

\[6\]

\[7\]

Representing equation (ii) in algebraic form:

\[x=3y+6\]

Solution table:

\[x\]

\[6\]

\[3\]

\[0\]

\[y\]

\[0\]

\[-1\]

\[-2\]

Graphical representation:

Pair of linear lines in coordinate plane


2. The coach of a cricket team buys \[\mathbf{3}\] bats and \[\mathbf{6}\] balls for \[\mathbf{Rs}\text{ }\mathbf{3900}\]. Later, she buys another bat and $\mathbf{3}$ more balls of the same kind for \[\mathbf{Rs}\text{ }\mathbf{1300}\]. Represent this situation algebraically and geometrically.

Ans: Assuming that the cost of bat and ball be \[x\] and \[y\] respectively.

Writing the algebraic representation using the information given in the question:

\[3x+6y=3900\]

\[x+3y=1300\]

Solution table for \[3x+6y=3900\]:

\[x=\frac{3900-6y}{3}\]

\[x\]

\[300\]

\[100\]

\[-100\]

\[y\]

\[500\]

\[600\]

\[700\]

Solution table for \[x+3y=1300\]:

\[x=1300-3y\]

\[x\]

\[1000\]

\[700\]

\[400\]

\[y\]

\[100\]

\[200\]

\[300\]

Graphical representation:


Pair of linear lines crossing each other at point (1300,0)


3. The cost of \[\mathbf{2}\text{ }\mathbf{kg}\] of apples and \[\mathbf{1}\text{ }\mathbf{kg}\] of grapes on a day was found to be \[\mathbf{Rs}\text{ 160}\]. After a month, the cost of \[\mathbf{4}\text{ }\mathbf{kg}\] of apples and \[\mathbf{2}\text{ }\mathbf{kg}\] of grapes is \[\mathbf{Rs}\text{ }\mathbf{300}\]. Represent the situation algebraically and geometrically.

Ans: Assuming that the cost of \[1kg\] of apples and \[1kg\] of grapes be \[x\] and \[y\] respectively.

Writing the algebraic representation using the information given in the question:

\[2x+y=160\]

\[4x+2y=300\]

Solution table for \[2x+y=160\]:

\[y=160-2x\]

\[x\]

\[50\]

\[60\]

\[70\]

\[y\]

\[60\]

\[40\]

\[20\]

Solution table for \[4x+2y=300\]:

\[y=150-2x\]

\[x\]

\[70\]

\[75\]

\[80\]

\[y\]

\[10\]

\[0\]

\[-10\]

Graphical representation:

Pair of linear lines parallel to each other.

NCERT Solutions For Class 10 Chapter 3 Maths Exercise 3.1

Learn More about Pair of Linear Equations in Two Variables

Before a student can write class 10 maths ch 3 ex 3.1 solutions, he or she should know about the basics of the chapter. In this section, students will be able to learn about those concepts.

According to experts, linear equations in two variables are used for explaining the geometry of lines or the graph of two lines. The graph is plotted to solve any given equation. It should also be noted that linear equations represent a straight line. The plotting of graphs will also help in solving equations that contain unknown variables.

An equation is also known as a linear equation in two variables if it is written in the form of ax + by + c = 0. In this basic form, a, b, and c are real numbers, and x and y are the coefficients. For example, 10x + 5y = 4 is a linear equation in two variables. This information is important for writing class 10 maths ex 3.1 solutions.

When it comes to linear equations in two variables, then there are infinitely many solutions. According to NCERT Solutions for Class 10 maths ex 3.1, if an individual wants to solve a linear equation in two variables, then for that, the values of the equations have to be known. The substitution method should be followed in that case.

There are also various cases that one can come across when writing class 10 maths chapter 3 exercise 3.1 solutions. Some of those cases are discussed below.


  • Unique Solutions

The solution will be unique for any linear equation in two variables if the variables intersect one another at a single point. The slope of the line that is formed by the two equations should also not be equal.

This means that if m1 and m2 are the two slopes of equations of two lines in two variables, then the equations will have a unique solution if:

m1 ≠ m2


  • No Solution

The equations will have no solution if the two linear equations have equal slope values. This means that the lines are parallel to one another and do not intersect. This further refers to the fact that:

m1 = m2


Download Exercise 3.1 Class 10 Maths NCERT Solutions

If you are a class 10 student who wants to score good marks, then you should download class 10 maths chapter 3 exercise 3.1 solutions. It is advised that students should learn the techniques that were used to solve the questions in this exercise.

There are also other exercises in chapter 3, including exercise 3.2, exercise 3.3, exercise 3.4, exercise 3.5, and exercise 3.6. Students should also solve those exercises. If you don’t know the answer to the questions in other exercises, then you can also find solutions for those questions.


Why Should You Get Class 10 Maths Ex 3.1 Solutions from Vedantu?

There are a number of reasons why you should choose to download class 10 chapter 3 exercise 3.1 solutions from Vedantu. And some of those reasons are mentioned below.

  • We provide students with live online classes.

  • We also solve any questions or queries that students might have related to different subjects and chapters.

  • All answers are 100% accurate and reliable.

  • Every answer is accompanied by an explanation section. The explanation section highlights the thought process that the subject matter expert followed to arrive at the correct answer.

  • Class 10 maths ch 3 ex 3.1 solutions prepare students for the final examination. This helps students to score the best possible marks.

 

NCERT Solutions for Class 10 Maths Chapter 3 Exercises

FAQs on NCERT Solutions for Class 10 Maths Chapter 3: Pair of Linear Equations in Two Variables - Exercise 3.1

1. Can I download NCERT solutions for class 10 maths chapter 3 exercise 3.1 from Vedantu even if my internet connection is not that fast?

Yes, all students can download class 10 chapter 3 maths exercise 3.1 irrespective of the speed and quality of internet connection that he or she might have. This is because chapter 3 maths class 10 exercise 3.1 solutions are available in a pdf file that is small in size and is also easy to download.


2. Is the file containing class 10 maths exercise 3.1 solutions available for free from Vedantu?

Yes, any student can download NCERT solutions class 10 maths chapter 3 exercise 3.1 pdf file from Vedantu for free. All you have to do is simply install the Vedantu app and click on the link of the NCERT maths class 10 chapter 3 exercise 3.1. You can also find the answer to other chapters and subjects on Vedantu. All solutions are available for free.

3. How can I solve linear equations in two variables?

You can find the answer by the elimination methods when it comes to a system of linear equations in two variables.

4. How many solutions are there when it comes to linear equations in two variables?

For linear equations in two variables, there are infinite solutions.

5. What are the coefficients of the equation 3x - 6y = -13?

In this equation, the coefficient of x is 3, and the coefficient of y is -6.

6. How many questions are there in exercise 3.1 of 10th Maths?

There are three questions in exercise 3.1 of NCERT CBSE Class 10 Maths. The chapter deals with a pair of linear equations in two variables. It is important and needs to be studied properly as this is the first time students are dealing with simultaneous equations as part of their syllabus. The elimination method and the substitution method can be used to solve all sums. If you are looking for NCERT solutions for this exercise visit the page NCERT Solutions for Class 10 Maths Chapter 3 on the Vedantu website or download them from the Vedantu app at free of cost.

7. How many examples are based on exercise 3.1 of class 10th mathematics?

All the examples in the first section of the chapter deal with questions similar to those asked in exercise 3.1 of Class 10 Mathematics. Linear equations in two variables are used for explaining the geometry of lines and a graph is plotted to solve any given equation. Any such linear equation can have infinite solutions. To come to a particular solution, students need to be provided with the values of the equation. 

8. What formulas are important from this chapter?

The NCERT Class 10 Maths Chapter 3 Pair is based on Linear Equations in Two Variables. It is very important to remember that the equation must be put in the form or formula of ax + by + c = 0. A and b themselves should not be zero. After this only, a linear equation is formed in the two variables of x and y. You must use this formula to solve questions. 

9. What study plan should I follow to score well in this chapter?

You must follow your NCERT textbook thoroughly to understand the basics of the chapter first. After this, you can refer to textbooks like RS Aggarwal and go through Vedantu NCERT Solutions Class 10 Chapter 3 Exercise 3.1. Some typical questions come from each chapter that have all been solved meticulously for you by Vedantu’s Subject Matter Experts. You can download NCERT solutions of all chapters for free of cost. With proper revision, you will pass with flying colours. 

10. Why do some linear equations have no solutions while others have many unique solutions?

The equations will have no solution if the slope values of both equations become the same. This means that the lines of the equations are parallel to one another and do not intersect. The solution will be unique if the variables intersect one another at a single point. The slope of the line that is formed by the two equations should also not be equal in order to obtain a unique solution.