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NCERT Solutions for Class 10 Maths Chapter 3 Ex 3.6 

 

NCERT Solutions for Class 10 Maths Chapter 3 Ex 3.6 have all the solutions for this exercise based on the latest CBSE syllabus. The sixth exercise of Class 10 Maths Chapter 3 Pairs of Linear Equations with Two Variables is based on equations reducible to pairs of linear equations with two variables. There are 2 questions in this exercise and both of them are important for board exam preparation. 

 

The askIITians Maths experts have created step-by-step solutions for Ex 3.6 for your complete conceptual understanding of the chapter. The topic introduced in this exercise is new and hence can be a little tricky for you. Our easy to understand NCERT Solutions will help you master this exercise in no time. Let us see what else is included in this exercise and how you can download the NCERT Solutions for Ex 3.6 of Class 10 Maths Chapter 3. 

About NCERT Class 10 Maths Chapter 3 Ex 3.6 

 

Linear Equation with Two Variables: An equation which can be put in the form: ax + by + c = 0, where a, b and c are real numbers (a, b ≠ 0) is called a linear equation in two variables ‘x’ and ‘y’. 

 

Pair of Linear Equation with Two Variables: General form of a linear pair of equations in two variables is: a1x + b1y + c1 - 0 and a2x + b2y + c2 = 0

where a1 b1, c1, a2, b2, c2 are real numbers. 

 

Solution of Pair of Linear Equations in Two Variables: Pair of linear equations can be solved using two methods: 

  1. Graphical Method 
  2. Algebraic Method 

In the graphical method, we observe the graphs of the two equations based on the following: 

  1. If the graphs of two equations of a system intersect at a point, the system is said to have a unique solution. In other words, the pair of linear equations is consistent.
  2. If the graphs of two equations of a system are two parallel lines, the system is said to have no solution. In other words, the pair of linear equations is inconsistent.
  3. When the graphs of two equations of a system are two coincident lines, the system is said to have infinitely many solutions. In other words, the pair of linear equations is consistent and dependent.

The algebraic method of solving a pair of linear equations includes three methods: 

  1. Substitution 
  2. Elimination 
  3. Cross-multiplication 

The solutions of a pair of linear equations in two variables depend upon: 

  1. If a1/a2 ≠ b1/b2, then the pair of linear equations is consistent,
  2. If a1/a2 = b1/b2, then the pair of linear equations is inconsistent,
  3. If a1/a2 = b1/b2 = c1/c2, then the pair of linear equations is consistent and dependent. 

Reducing equations to pairs of linear equations in two variables

Some equations are not linear but can be reduced to linear form. For instance, consider the following equations: 

ax+ by = c

We can convert this equation to linear equation in two variables (ax + by + c = 0):

Let 1x = m and 1y = n

Now after the substitution, we can write the equation in linear form as: 

am + bn = c 

Download Free NCERT Solutions for Class 10 Maths Chapter 3 Ex 3.6 

Chapter 3 Pairs of Linear Equations in Two Variables is a scoring chapter if you practice all its exercises thoroughly. By practising the questions of this exercise you can hone your arithmetic skills. In case you face any difficulty, our NCERT Solutions will provide you with the right guidance. Let us see what kind of problems are included in this exercise:

Ex 6.2 Q1: The first question of this exercise includes 8 subparts. In each subpart, you are given two different equations. You have to convert them into a linear form. We have solved each equation in a stepwise manner so that you can understand how to solve this exercise. 

Ex 6.2 Q2: In this question, you are given different word problems. You have to read them carefully, formulate pairs of linear equations and find their respective solutions. This is a tricky question as you have to prepare the linear equations on your own. Check our NCERT Solutions and match your answers. 

Why must you download NCERT Solutions for Class 10 Maths Chapter 3 Ex 3.6? 

  • NCERT solutions include stepwise explanations for all questions so you will have no doubts in the exercise. 
  • These solutions are prepared by our expert faculty members based on the latest CBSE syllabus and exam pattern. 
  • You can study these solutions independently at your own pace and convenience. 

Download NCERT Solutions for all exercises of Chapter 3 Pairs of Linear Equations in Two Variables:

  • NCERT Chapter 3 Class 10 Maths Ex 3.1 Solutions - 3 Questions
  • NCERT Chapter 3 Class 10 Maths Ex 3.2 Solutions - 7 Questions
  • NCERT Chapter 3 Class 10 Maths Ex 3.3 Solutions - 3 Questions
  • NCERT Chapter 3 Class 10 Maths Ex 3.4 Solutions - 2 Questions
  • NCERT Chapter 3 Class 10 Maths Ex 3.5 Solutions - 4 Questions
  • NCERT Chapter 3 Class 10 Maths Ex 3.6 Solutions - 2 Questions
  • NCERT Chapter 3 Class 10 Maths Ex 3.7 Solutions - 8 Questions

NCERT Class 10 Maths Chapter 3 Ex 3.6 FAQs

  1. What is the main topic of NCERT Class 10 Maths Chapter 3 Ex 3.6?

The sixth exercise of NCERT Class 10 Maths Chapter 3 is based on the concept of reducing algebraic equations into linear equations. This is an interesting exercise with 3 examples and 2 unsolved problems. 

  1. How can I download NCERT Solutions for Class 10 Maths Chapter 3? 

You can find exercise-wise NCERT Solutions for Chapter 3 Pairs of Linear Equations in Two Variables on the askIITians website. You can download them for free in PDF form and study them whenever you want. 

  1. How can askIITians help me in Class 10 Maths? 

askIITians provides NCERT Solutions, revision notes, extra questions, previous year questions, mind maps, flashcards, and many interesting study resources for Class 10 Maths. You can also enrol in our Class 10 Maths online coaching and study from the comfort and safety of your homes. 


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