Maharashtra Board SSC Science Books

August 10, 202239 Insightful Publications

**NCERT Solutions for Class 10 Maths Chapter 3: **The Class 10 Maths NCERT Solutions Chapter 3 deals with Pair of Linear Equations in Two Variables. The topic is easy, and students can obtain full marks if they practice answering the NCERT questions from this chapter. So, we have provided the detailed CBSE NCERT Solutions Class 10 Maths Chapter 3 in this article. They involve questions that test and improve your logical reasoning and analytical abilities for speed and accuracy.

The solutions for NCERT Chapter 3 Maths Class 10 Linear Equations Two Variables are based on the latest CBSE syllabus and exam pattern guidelines. Moreover, they have been provided in downloadable PDF format for students to refer offline. Scroll down to get NCERT Solutions for Class 10 Maths Chapter 3 and links to other valuable resources.

NCERT Solutions for Class 10 Maths Chapter 3 discusses *Pair of Linear Equations in Two Variables* and provides you with a good understanding of the problems in the chapter.

The NCERT Solutions Class 10 Maths Chapter 3 is very interesting and students can score full marks in this chapter easily. Students can download the exercise-wise NCERT Solutions for Class 10 Maths for Chapter 3 Linear Equations Two Variables from the following table:

Exercise 3.1 Class 10 | Pair of Linear Equations in Two Variables |

Exercise 3.2 Class 10 | Graphical Method of Solution of a Pair of Linear Equations |

Exercise 3.3 Class 10 | Substitution Method |

Exercise 3.4 Class 10 | Elimination Method |

Exercise 3.5 Class 10 | Cross-Multiplication Method |

Exercise 3.6 Class 10 | Equations Reducible to a Pair of Linear Equations in Two Variables |

You can find Class 10 Maths Chapter 3 exercise 3.5 solutions and Class 10 Maths Chapter 3 Exercise 3.3 solutions on the Embibe app and website.

**Check**– **Algebra Formulas for Class 10**

You can find the CBSE 10th Maths Chapter 3 solutions below. You can also download CBSE Class 10 Maths Chapter 3 Solutions PDF Pair of Linear Equations in Two Variables from the link given below to practice offline and learn the Chapter 3 Maths Class 10 Formula for better preparation. You can refer to the PDF or download it for future reference.

NCERT solutions provided here are prepared by top academic experts at Embibe. These solutions for Exercise 3.1 Class 10 to Exercise 3.6 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.

**Q. Form the pair of linear equations in the following problem and find their solution graphically.10 students of Class X took part in a Mathematics quiz. If the number of girls is 4 more than the number of boys, find the number of boys and girls who took part in the quiz.Solution:** Let the number of girls in the class be x and the number of boys in the class be y.

As per the given conditions

x+y=10 (1)

x-y=4 (2)

x+y=10⟹x=10-y

Two solutions to this equation are:

x 0 10

y 10 0

x-y=4⟹x=4+y

Two solutions to this equation are:

x 2 4

y -2 0

**Q: On comparing the ratios a1a2,b1b2 and c1c2, find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident:5x-4y+8=07x+6y-9=0Solution**: Given,

5x-4y+8=0

7x+6y-9=0 Comparing the given pair of equations with a1x+b1y+c1=0 and a2x+b2y+c2=0, we get,

a1=5,b1=-4,c1=8, and a2=7,b2=6,c2=-9 So, a1a2=57 and b1b2=-46=-23; Since, a1a2≠b1b2 Hence, the given pair of equations intersect at exactly one point.

Also, Check

**1st Chapter: Real Numbers****2nd Chapter: Polynomials****4th Chapter: Quadratic Equations****5th Chapter: Arithmetic Progressions****6th Chapter: Triangles****7th Chapter: Coordinate Geometry****8th Chapter: Introduction to Trigonometry****9th Chapter: Some Applications of Trigonometry****10th Chapter: Circles****11th Chapter: Constructions****12th Chapter: Areas Related to Circles****13th Chapter: Surface Areas and Volumes****14th Chapter: Statistics****15th Chapter: Probability**

**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 Class 10. 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.

**Download Pair of Linear Equations in Two Variables NCERT Solutions**

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.

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 exams.
- These solutions can be used as quick revision material before a test or an exam.
- The NCERT solutions by Embibe are also very helpful in preparing for different competitive exams, NTSE, Olympiads, etc.
- The NCERT Solutions for all the subjects are available for free at Embibe.

*Q1. 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.***Ans.** k = 6

*Q2. 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?***Ans.** The lines will intersect at (- 4, – 5).

*Q3. 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***Ans.** a = 3 and b = 1

*Q4. Find the value of ‘x’ in the equation x + 2y = 10 if the value of y is given as 6.***Ans.** x = – 2

*Q5. What is the position of the graph of equation x = – 2 with respect to the y-axis?***Ans.** The graph of the given equation will be parallel to the y-axis.

**Q6.** **How many exercises are covered in CBSE NCERT Class 10 Maths Chapter 3****and how can I download these CBSE 10th Maths Chapter 3 Solutions?****Ans.** NCERT Class 10 Maths Chapter 3 is about Pair of Linear Equations in Two Variables. This chapter has a total of seven exercises. The NCERT Solutions for Class 10 Maths Chapter 3 have been created by experts at Embibe. You can download the solutions in the PDF format given in this article for future reference.

*Q7. What is the graphical representation of the given equations 7x – y = 5 and 21x – 3y = 10?***Ans.** These lines are parallel to each other on the graph.

*Q8. Find the other equation from the given pair of dependent linear equations if one of them is –5x + 7y – 2 = 0.***Ans.** 10x – 14y = –4

*Q9. 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.***Ans. **The present age of the father is 36 and the age of the son is 6.

*Q10. How many solutions are possible for the given pair of equations 3x – 5y = 7 and – 6x + 10y = 7?***Ans.** No solution.

*Q11. You are given two numbers which are in the ratio of 5:6. Find the numbers if the ratio becomes 4:5 after subtracting 8 from each of the numbers.***Ans.** The numbers are 40 and 48.

*Q.12. Where can I get Class 10th Maths NCERT Solution for free?*** Ans.** Students can download the NCERT Solutions Class 10 Maths Chapter 3 in PDF format from the link given in this article.