# RD Sharma Class 10 Chapter 3 Solutions (Pair of Linear Equations in Two Variables)

RD Sharma Class 10 Maths Solutions Chapter 3- Pair of Linear Equations in Two Variables is prepared to help you learn and understand the chapter better. This chapter has concepts such as the meaning of an equation, the meaning of a linear equation, linear equation in two variables in general form, representing linear equations for a word problem, solution of a linear equation in 2 variables, a geometrical representation of a linear equation, plotting a straight line, nature of two straight lines in a plane, comparing the ratios of coefficients of a linear equation, graphical method of finding the solution of a pair of linear Equations, the algebraic solution with elimination method, cross-multiplication method, substitution method, and graphical method. It also covers equations reducible to a pair of linear equations in 2 variables.

This chapter consists of 11 exercises with more than 100 questions. Questions are asked in these exercises cover all corners of the chapter. Our RD Sharma solutions are step by step solutions that answer all questions from all exercises in a simple language, accurately and precisely. They give a good amount of practice to help you become thorough with the chapter and clear all your doubts. They cover a wide range of questions and question types important from Class 10 board exam point of view to help you get well acquainted with the board exam pattern.

Our Maths shortcut techniques help you learn faster and better. They also help you remember for a longer period of time. With our RD Sharma Class 10 Maths Solutions Chapter 3-Pair of Linear Equations in Two Variables,** **you can improve your conceptual knowledge and perform exceptionally well in your board exams.

## Class 10 Maths Pair of Linear Equations in Two Variables

RD Sharma Class 10 Maths Solutions Chapter 3-Pair of Linear Equations in Two Variables discuss the details on linear equations in two variables. Some of the topics contained in this chapter have been discussed below.

**Introduction**

This part of the chapter explains to you the meaning of equations and linear equations with relevant examples and introduce you to various techniques to solve them.

**General Form of a Linear Equation in Two Variable**

This section of RD Sharma Class 10 Maths Solutions Chapter 3 – Pair of Linear Equations in Two Variables, introduces you to the general form of linear equations in two variables.

Here, px + qy + r =0, where p and q cannot simultaneously be zero.

You’ll also learn how to represent linear equations for a word problem. You will also be taught about the solution of a linear equation in two variables, and here you will learn how to make the equation equal on both sides.

**Geometrical Representation of a Linear Equation**

This section of the chapter will make you understand that a linear equation in two variables can be represented as a straight line. This section also helps you learn how to plot a straight line on a graph.

**All About Lines**

This part of Class 10 Maths Pi of Linear Equations in Two Variables, makes you understand about the general form of a pair of linear equations in two variables and nature of two straight lines in a plane. It teaches you about three different possibilities for plotting a pair of two straight lines on a plane. They are as follows.

- Lines intersect exactly at one single point
- Parallel lines
- Coincident lines

**Algebraic Solution**

This portion of RD Sharma Solutions for Class 10 Maths Chapter 3-Pair of Linear Equations in Two Variables, teaches you about various methods of solving a pair of linear equations such as elimination method, cross multiplication method, substitution method and graphical method.

**Solving Linear Equation**

This section of the chapter explains you about the equations reducible to a pair of linear equations in two variables. Certain equations could be reduced to a linear equation by applying a substitution method and then solved.

For Example: Let us consider, **
**4/x+6/y=8

**9/x−3/y=6**

**When we apply substitution to the above equation,**

**1/x = u and 1/y = v**

**The pair of equations reduces to**

**4u + 6v = 8**

**9u – 3v = 6**

**The above-mentioned equations pair might be solved, and after that, you get back to the substitutions to find the values of X and Y.**

### RD Sharma Class 10 Maths Chapter 3 Exercises

There are a total of 11 exercises with around 129 questions at the end of the chapter. Below is a brief overview:

**Exercise 3.1**

- This exercise consists of 3 questions in total. All three questions are scenario-based questions, and they are based on algebraic and graphical representations.

**Exercise 3.2**

- This exercise consists of 21 questions. From question 1 to question 10, you have to solve them by a system of equations with the help of the graphical method. All the questions are of the same pattern.
- For question 11 to question 14 need, you to show that the given systems of the equations have infinitely many solutions.
- Question 15 to question 21, asks you to solve the given equation in a graphical method, and you have to show that the given systems of the equation are inconsistent.

**Exercise 3.3**

- This exercise consists of 26 questions completely. All the questions asked in this exercise are similar to each other. This whole exercise consists of questions that need you to find a solution for a consistent pair of linear equations. This exercise covers the algebraic solution concept.

**Exercise 3.4**

**This exercise consists of 14 questions in total. This complete exercise focuses on the topic of solving a pair of linear equations with the application of cross multiplication method.**

**Exercise 3.5**

- This exercise consists of 18 questions completely. Questions from this exercise are based on finding the values of the given system of linear equations having infinitely many solutions, unique solution or no solution.

**Exercise 3.6**

- This exercise consists of 7 questions. All the 7 questions in this exercise are scenario-based questions, and this exercise mainly focuses on algebraic solution concept.

**Exercise 3.7:**

- Altogether, this exercise consists of 8 questions. All the 8 questions are word problems that cover various topics of the chapter

**Exercise 3.8:**

- This exercise consists of 5 questions. All the questions are word problems, and they need you to find the fractions by solving the given linear equations

**Exercise 3.9:**

- On the whole, this exercise consists of 6 questions. All are word problems, and they focus on cross multiplication method of solving a linear equation method.

**Exercise 3.10:**

- This exercise consists of 9 questions. All the questions are word problems. This exercise is based on equations reducible to a pair of linear equations.

**Exercise 3.11:**

- This exercise consists of 12 questions. All are word problems which mainly focus on the general form of linear equations.

### Benefits of RD Sharma Class 10 Maths Chapter 3

- Our RD Sharma Class 10 Maths Solutions Chapter 3- Pair of Linear Equations cover all the main topics and sub-topics in details and answer all exercise questions given at the end of the chapter in a step by step manner
- They are easy to understand, precise, and a hundred per cent accurate.
- They help you learn quickly, effectively and retain more.
- With the help of these solutions, you will be developing a strong conceptual foundation that will help you learn more complex topics in higher classes
- Our RD Sharma solutions clear all your doubts, help you become thorough with all the concepts of the chapter and score high marks in your Class 10 board exams.
- They have been devised in a manner to make learning more fun, interesting, stimulating, interactive and a stress-free process.