**NCERT Solutions For Class 10 Maths Chapter 3: ***Pair of Linear Equations In Two Variables* is a very important chapter in the 10th Maths syllabus and it consists of a variety of problems to solve**. **To help you with solving them, we bring you this article with the detailed NCERT Solutions for Class 10 Maths Chapter 3 – Pair of Linear Equations In Two Variables. The NCERT solutions provided here are prepared by top academic experts at Embibe. These solutions will help you revise the whole syllabus and score well in the board exams.

You can even download these NCERT solutions in the form of PDF and solve the problems offline when required. We are providing the step-by-step solutions to all the exercise problems which are as per the NCERT textbook. Solving these problems will help you have a better understanding of the chapter and will improve your confidence. Read on to find the CBSE NCERT Solutions for Class 10 Maths Chapter 3.

**PRACTICE CBSE 10th MATHS CHAPTER 3 IMPORTANT QUESTIONS HERE**

**NCERT Solutions For Class 10 Maths Chapter 3: Pair Of Linear Equations In Two Variables**

Before getting into the details of CBSE NCERT Solutions For Class 10 Maths Chapter 3, let’s have a look at the constituent topics of the chapter:

Section Name | Topic Name |

3.1 | Introduction |

3.2 | Pair of Linear Equations in Two Variables |

3.3 | Graphical Method of Solution of a Pair of Linear Equations |

3.4 | Algebraic Methods of Solving a Pair of Linear Equations |

3.4.1 | Substitution Method |

3.4.2 | Elimination Method |

3.4.3 | Cross-Multiplication Method |

3,5 | Equations Reducible to a Pair of Linear Equations in Two Variables and |

3.6 | Summary |

**NCERT Solutions For Class 10 Maths Chapter 3: Pair Of Linear Equations In Two Variables (Solutions PDF)**

You can find the solved exercises for 10th Maths Chapter 3 below. You can also download the **CBSE Class 10 Maths Chapter 3 Solutions PDF** from the link given below to practice offline*.*

**Download NCERT Solutions PDF For 10th Maths Chapter 3 Here**

**CBSE Class 10 Maths Chapter 3: Pair Of Linear Equations In Two Variables**

**Chapter Description: **Linear equations in two variables are equations that can be expressed as *ax + by + c = 0* where a, b and c are real numbers and both a and b are non-zero. The solution of such equations is a pair of values for x and y which makes both sides of the equation equal.

Let’s look at the solutions of some linear equations in two variables. Consider the equation 2x + 3y = 5. There are two variables in this equation, x and y.

**Scenario 1:**Let’s substitute x = 1 and y = 1 in the LHS of the equation. Hence, 2(1) + 3(1) = 2 + 3 = 5 = RHS. Hence, we can conclude that x = 1 and y = 1 is a solution of the equation 2x + 3y = 5.**Scenario 2:**Let’s substitute x = 1 and y = 7 in the LHS of the equation. Hence, 2(1) + 3(7) = 2 + 21 = 23 ≠ RHS. Therefore, x = 1 and y = 7 is not a solution of the equation 2x + 3y = 5.

Geometrically, this means that the point (1, 1) lies on the line representing the equation 2x + 3y = 5 and the point (1, 7) does not lie on this line. In simple words, every solution of the equation is a point on the line representing it.

To generalize, each solution (x, y) of a linear equation in two variables, ax + by + c = 0, corresponds to a point on the line representing the equation and vice versa.

This chapter consists of seven exercises with the last exercise including an optional exercise. By the end of chapter 3, you will learn to solve pair of linear equations by graphical method (which will be solved on graph sheets) and algebraic method (using three methods). Lastly, you will also be able to solve the equations which are reducible to a pair of linear equations. The chapter has plenty of examples and exercise questions. So, go through the NCERT solutions for Class 10 Maths Chapter 3 if you have any doubts.

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### Key Features Of Embibe’s NCERT Solutions For 10th Maths Chapter 3

Given below are some of the key features of **NCERT solutions** by Embibe:

- The experts at Embibe prepared these NCERT solutions in a simple and lucid language so that the students can learn the topics without any difficulty.
- All the NCERT solutions have been prepared in accordance with the revised CBSE syllabus and the latest NCERT guidelines.
- With the help of these solutions, students can learn the correct method of answering questions in the exams.
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### FAQs On NCERT Solutions For Class 10 Maths Chapter 3: **Pair Of Linear Equations In Two Variables**

Some of the frequently asked questions are given below:

**Q1. What is the graphical representation of the given equations 7x – y = 5 and 21x – 3y = 10?**

A. These lines are parallel to each other on the graph.

**Q2. Find the other equation from the given pair of dependent linear equations if one of them is –5x + 7y – 2 = 0.**

A. 10x – 14y = –4

**Q3. How many solutions are possible for the given pair of equations 3x – 5y = 7 and – 6x + 10y = 7?**

A. No solution.

**Q4. If the pair of equations x = – 4 and y = – 5 are plotted on a graph, the lines representing these equations will intersect at which point?**

A. The lines will intersect at (- 4, – 5).

**Q5. You are given two numbers which are in the ratio 5:6. Find the numbers if the ratio becomes 4:5 after subtracting 8 from each of the numbers.**

A. The numbers are 40 and 48.

**Q6. What is the position of the graph of equation x = – 2 with respect to the y-axis?**

A. The graph of the given equation will be parallel to the y-axis.

**Q7. Find the values of a and b for which the following pair of equations has an infinite number of solutions: x + 2y = 1 and (a – b)x + (a + b)y = a + b – 2**

A. a = 3 and b = 1

**Q8. Find the value of ‘x’ in the equation x + 2y = 10 if the value of y is given as 6.**

A. x = – 2

**Q9. You are given a pair of equations 3x + 5y = 0 and kx + ly = 0. Find the value of ‘k’ for which the equations have a non-zero solution.**

A. k = 6

**Q10. Find the present ages of a father and the son if the father’s age is six times his son’s age and after four years, the father’s age will be four times the age of his son.**

A. The present age of the father is 36 and the age of the son is 6.

### Practice 10th Maths Lessons & Questions With Embibe

We have now provided you with all the details on CBSE NCERT Solutions For Class 10 Maths Chapter 3. Go through the step-by-step solutions and practice well in order to make the best use of it. Try and solve the problems on your own and refer to the solutions only if you get stuck in between. This will help you to learn the methods to solve the questions which can be extended further by practicing other questions too. You can also take a free **Pair of Linear Equations In Two Variables mock test** on Embibe. With the help of this test, you can strengthen your conceptual knowledge and test-taking skills.

Embibe offers various other resources for Class 10 students in addition to the NCERT Solutions. At Embibe, you can solve **CBSE Class 10 Practice Questions** or take **Class 10 Mock Tests** for free. So, utilize the solutions, books, practice questions, and mock tests by Embibe and boost your scores.

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