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Important Questions for CBSE Class 10 Maths Chapter 3 - Pair of Linear Equations in Two Variables 2024-25

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Last updated date: 17th Apr 2024
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MVSAT 2024

CBSE Class 10 Maths Important Questions Chapter 3 - Pair of Linear Equations in Two Variables - Free PDF Download

The beginning of a student's career starts with their first board exam of class 10. Class 10 results determine a student's career and their focus on the subject they want to study and proceed with. We say mathematics is the key to all topics, and it only gets harder with growing class. It is the only subject that requires a lot of practice and concentration. 

Like other subjects, you cannot learn mathematics. A lot of practice, concentration, and knowledge are the only ways to get the perfect score. Therefore, everyday practice and concentration will help one to get through the exam easily. 

Here we discuss the third chapter of class 10 maths, Linear equations. It is one of the introductory mathematics branches that will help the students excel in competitive exams. The Pair of Linear Equations in two variables is an important chapter and consists of various maths problems. We have assembled some important questions for class 10 maths chapter 3, which will help the students have a thorough revision before the exams. 

Download CBSE Solutions for all subjects for free from Vedantu. Students can register and download Class 10 Maths and Class 10 Science NCERT Solutions and solutions of other subjects for free.


Download CBSE Class 10 Maths Important Questions 2024-25 PDF

Also, check CBSE Class 10 Maths Important Questions for other chapters:

CBSE Class 10 Maths Important Questions

Sl.No

Chapter No

Chapter Name

1

Chapter 1

Real Numbers

2

Chapter 2

Polynomials

3

Chapter 3

Pair of Linear Equations in Two Variables

4

Chapter 4

Quadratic Equations

5

Chapter 5

Arithmetic Progressions

6

Chapter 6

Triangles

7

Chapter 7

Coordinate Geometry

8

Chapter 8

Introduction to Trigonometry

9

Chapter 9

Some Applications of Trigonometry

10

Chapter 10

Circles

11

Chapter 11

Constructions

12

Chapter 12

Areas Related to Circles

13

Chapter 13

Surface Areas and Volumes

14

Chapter 14

Statistics

15

Chapter 15

Probability

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Important Questions for CBSE Class 10 Maths Chapter 3 - Pair of Linear Equations in Two Variables

Class 10 is a crucial year for every student's career and an important step towards their future. No matter which subject the student wants to study, it is impossible to accomplish the year without proper concentration and knowledge. 

Every year, thousands of students choose mathematics for their career and fail to score good grades due to lack of practice. Mathematics requires daily exercise and a routine that every student should follow. 

Without proper practice, it is not possible to understand where to place which formula and solve the problems. Here, we have assembled extra questions for class 10 maths chapter 3

These PDF questions are prepared by Vedantu experts and are free for the students to download and practice. The teachers have prepared the question-answer set for the students according to new CBSE guidelines. The students can easily cover the entire chapter and all sorts of questions coming for their final exams. These questions cover most of the topics and are extremely reliable. It will boost your confidence and help you solve all types of questions that the examiners can set. 


Chapter 3 Maths Class 10 Important Questions

Mathematics is not an easy subject that anyone can solve just by studying before a few days of examination. Especially, class 10 is crucial with high-level mathematics problems for the students to solve. Therefore, daily practices will help students memorize the formulas and understand the types of issues that might come up during their finals. Expert mathematicians of Vedantu have prepared a set of important questions of chapter 3 Maths class 10, which will help the students revise the chapter easily. The pdf is free for the students who register for the site. 


What are Linear Equations?

Equations with first order are known as linear equations. The word linear defines the equation is in a line of the coordinate system. Therefore, any equation lying in a straight line is known as a linear equation. y=mx+b resembles the definition of a straight line where b is the intercept and m is the slope of the line. These equations consist of the highest exponent of variables as one and hence, are known as first-degree equations.

There are various types of linear equations. When an equation has only one variable or a homogeneous variable, then that type is known as a linear equation with one variable. In other words, an equation in a line is achieved by relating zero to any field of linear polynomial from which we can obtain the coefficients id known as a linear equation with one variable. 

The answers of linear equations produce values that make a true equation when exchanged with unknown values. There is only one solution available for one variable, like x+2=0. However, when it comes to two variables linear equation, the Euclidean plane's answer is calculated as Cartesian coordinates. 


Forms of Linear Equation

A line is determined in an X-Y plane through various forms. Here, we have a list of some common conditions which we use to solve linear equations. 

  • Slope Intercept Form

  • General Form

  • Intercept Form

  • Two-point Form

  • Point Form


The Standard Form of Linear Equations

The combination of variables and constants form a linear equation. A linear equation with one variable is depicted as ax+b=0, where x is a variable, and a≠0. 

The standard form of linear equation with two variables is depicted as ax+by+c=0, where a is not equal to zero, b is not equal to zero, and x and y are variables. 

The standard form of a linear equation with three variables is depicted as ax+by+cz+d=0, where a, b and c are not equal to zero and x, y, z are variables. 

  • Slope Intercept Form

The most common way to solve linear equations is in the slope-intercept form. It is represented as y=mx+c, where y and x are the x-y plane points, c is the intercept with a constant value and m is the slope of the line known as a gradient. 

For example, y=5x+9

Slope, m=5, and intercept=9.

  • Point Slope Form

Considering the points on the x-y plane, a straight line equation is formed as the linear equation. It is represented as y-1=m(x-x1), where the coordinates of the line are x1 and y1. The other way of representing it is y=mx+y1-mx1.

  • Intercept Form

The intercept form is represented when the axes of the lines intersect in two different points on the x-y plane and are neither parallel to the y-axis or the x-axis. In the equation, x/x0+y/y0=1, the values of x0 and y0 are not equal to zero. 

  • Two Point Form

Suppose (x1,y1) and (x2,y2) are two points, and only one line passes through these points, then the linear equation is represented as 

y-y1=[(y2-y1)/(x2-x1)](x-x1) where x1≠x2 and (y2-y1)/(x2-x1) is the slope of the line.


Solving Linear Equations with One Variable

To solve a linear equation, you must balance both sides of the equation. When you place the equality sign in between the equation, it denotes that the value on both sides of the equation is equal. The balanced equation requires specific ways of solving it as you cannot change anyone side's value. To find the value of x, the first step is to simplify both sides and then put all the x consonants on one side, finding out the value of x. 


Solving Linear Equations with Two Variables

There are different methods that you can use to solve linear equations with two variables. 

  • Substitution method

  • Cross multiplication method

  • Elimination method

  • Determinant methods

When looking for values of the variables like x and y, it is important to solve two sets of equations. Since a single equation can have an infinite amount of solutions. Suppose, ax+by+c=0 and dx+ey+f=0, where x and y are variables and a≠0, b≠0, c≠0, d≠0, and e≠0.


Class 10 Maths Chapter 3 Extra Questions For Students to Practice

  1. In the equation y=0, and y= -5, find the number of solutions. 

  2. Find the value of (x+y) from the two equations, ax+by=a²-b², and bx+ay=0. 

  3. Find if the following linear equations are inconsistent or consistent, 3x+2y=8, 6x-4y=9.

  4. Draw the graph of 2x=y+3, 2y=4x-6, and check if the equation has a unique solution. 

  5. Draw the equations on graph paper where the coordinates of the points intersect the lines at the y-axis. x+3y=6, 2x-3y=12. 

  6. Solve x and y: 10/x+y +2/x-y =4; 15/x+y - 5/x-y =-2

  7. Solve the pair of linear equations. 141x +93y =189; 93x+141y=45

  8. Solve by elimination method: 3x= y+5, 5x-y=11.

  9. Find the values of x and y: 27x+31y=85; 31x+27y=89

  10. Find two numbers that have a sun of 75 and a difference of 15.


Benefits of CBSE Class 10 Maths Chapter 3 Important Questions

Class 10 students often face trouble with mathematics, and they often find it difficult to score good marks. With so many chapters and the number of formulas, it is impossible to remember everything. This is the reason; the set of questions help the students to revise the chapters. 

  • The important question of ch 3 maths class 10 will help the students to practice last minute mathematics and revise the chapter covering all types of problems. 

  • The set of important questions involve every kind of questions that might come in the exams. 

  • Extra questions for class 10 maths chapter 3 is available for all the students on the Vedantu website.


Conclusion

Class 10 is a crucial year for every student, and covering all mathematics topics is important to score good grades. This set of important questions will help the students to cover all the issues and score good marks. 


Important Related Links for CBSE Class 10 Maths

FAQs on Important Questions for CBSE Class 10 Maths Chapter 3 - Pair of Linear Equations in Two Variables 2024-25

1. Where can we avail the Important questions for class 10 maths chapter 3 linear equations in two variables?

The most accurate and reliable  Important questions for class 10 maths chapter 3 linear equations in two variables are available on Vedantu as a free PDF download to help students. Prepared by subject matter experts these are one of the most reliable and irreplaceable study material for the students. With the Important questions, Vedantu provides students with mock papers, sample papers, solved previous years question papers along with NCERT Solutions along with answers to make studying as flawless as possible for the students. Along with these study materials, students can avail LIVE online classes on Vedantu to make they’re studying a more realistic and productive activity to obtain maximum results.

2.  What do the Important Questions for Class 10 Maths hold?

The important questions for Class 10 Maths hold all the questions that are important from the exam point of view. This is a very important material as they cover the topics which the students would tend to forget to study them or would have missed them during their study session. These questions cover most of the important topics and chapters in the form of solved questions that help students learn better. These important questions will help you to revise each and every important topic in the syllabus. Also, these important questions are a great way of revising and testing yourself once you finish studying the entire syllabus.

3. What is the general form of a Linear Equation in Two Variables? What is the Solution of a Linear Equation in 2 variables?

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


The solution of a linear equation in two variables is a pair of values, one for x and the other for y. These two values must make the two sides of the equation equal.


Eg: If 4x + y = 14, then (2,6) is one of its solutions as it satisfies the equation.


Note: A linear equation in two variables has infinite solutions.

4. What are the different ways of finding solutions to a linear equation in two variables?

The different ways of finding solutions to a linear equation in two variables are mentioned below:

  • Elimination method

  • Substitution method

  • Cross-multiplication method

  • Graphical method

5. What tips should be followed by a student to prepare Chapter 3 of Class 10 Maths?

For preparing Chapter 3 of Class 10 Maths, the following tips should be followed by the students:

  • Refer to the Maths NCERT book for understanding the concepts of Chapter 3 of Class 10 Maths.

  • Solve every exercise and example to comprehend the chapter in a better way.

  • Try to attend the school lectures as you will be able to understand the chapter more easily.

  • Go through the previous years question papers to know about the pattern of the exam.

6. What are the various topics included in Chapter 3 of Class 10 Maths?

The several concepts covered in Chapter 3 of Class 10 Maths are:

  • Introduction

  • Pair of Linear Equations in Two Variables

  • Discovering Solution Graphically for a Pair of Linear Equations

  • Solving a Pair of Linear Equations with the help of Algebraic Methods

            I. Substitution Method

            II. Elimination Method

            III. Cross-Multiplication Method

  • Reduction of a Set of Linear Equations in Two Variables

Students have to be thorough with these topics to solve questions related to the chapter.


7. What is the method of finding the existence of solutions for a pair of linear equations?

The Linear equations are represented by two lines in the graphical method. 

To find their solutions consider the following points:

  • If the pair of equations is consistent then the lines will cut each other at a common point. This means that these equations will have a unique solution.

  • There are infinitely many solutions for that pair of equations for which the two lines will coincide with each other. These equations are dependent.

  • The pair of equations will have no solution if the lines are parallel. In this case, these equations are inconsistent.

8. What is the basic concept behind the topic "Pair of Linear Equations in Two Variables"?

This topic is taken from Chapter 3 of Class 10 Maths. In this topic, students will learn about the general format for writing linear equations in two variables. The equation is presented in the form of "ax + by + c = 0" where a and b are non-zero and real numbers. The solution for the equations is defined as those values of x and y, which makes the two equations equal. As the equation is represented by a line, therefore, the solution of the equation is a point on that line.

9. Is it possible to download important questions of Chapter 3 of Class 10 Maths?

Yes, it is. Students can download the important questions of Chapter 3 of Class 10 Maths by following the given steps:

  • Visit the page-Important questions for Chapter 3 of Class 10 Maths.

  • Vedantu's official website will open.

  • After the opening of the website, you will see that the important questions of Chapter 3 of Class 10 Maths are available there.

  • On top of the provided important questions, you will discover the option of "Download PDF".

  • Click that option and the PDF file will be downloaded free of cost.

Students can also visit the Vedantu app to download the study material free of cost.