NCERT Solutions for Class 10 Maths Chapter 3 Ex 3.5

 

NCERT Solutions for Class 10 Maths Chapter 3 Ex 3.5 are created by the askIITians experts to help students in solving this exercise. The fifth exercise of the chapter is based on solving a pair of linear equations using the cross-multiplication method. This exercise includes 4 questions out of which the last question is the toughest of all. This exercise includes different word problems where you have to formulate the linear equations and find their solution using the cross-multiplication method.

 

askIITians NCERT Solutions provide you stepwise answers for all the questions of this exercise. This way you can resolve your doubts on your own and practise the exercise at your own pace. The NCERT Solutions for Class 10 Maths Chapter 3 Ex 3.5 are based on the latest CBSE Class 10 Maths syllabus and exam pattern. You can download these solutions for free in pdf form and refer to them as many times as you want. Let us see what is included in Ex 3.5 and how you can download its solutions. 

About NCERT Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 

 

In Chapter 3 of Class 10 Maths, you study different methods of solving a pair of linear equations in two variables. This includes the graphical method, substitution method, elimination method, and cross-multiplication method. You also study how to reduce equations to a pair of linear equations in two variables. Exercise 3.5 of Chapter 3 Pair of Linear Equations in Two Variables is about solving a pair of linear equations using the cross-multiplication method. Here are some important points that will help you solve this exercise:

 

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 the following: 

• If a1/a2 ≠ b1/b2, then the pair of linear equations is consistent,

• If a1/a2 = b1/b2, then the pair of linear equations is inconsistent,

• If a1/a2 = b1/b2 = c1/c2, then the pair of linear equations is consistent and dependent. 

Steps of solving a pair of linear equations using the cross-multiplication method: 

A pair of linear equations in two variables is given by a1x + b1y + c1 - 0 and a2x + b2y + c2 = 0 where a1 b1, c1, a2, b2, c2 are real numbers. 

Step 1: Write the pair of linear equations as: 

a1x + b1y + c1 = 0 –(1)

 a2x + b2y + c2 = 0 –(2)

Multiply equation (1) with b2 and equation (2) with b1, you will get:

 

b2a1x + b2b1y + b2c1 = 0 –(3)

b1 a2x + b1b2y + b1c2 = 0 –(4)

Subtract equation (4) from equation (3):

 

(b2a1 - b1 a2)x + (b2b1 - b1b2) y + (b2c1- b1c2) = 0 

The values of x and y are given by:

 

We can write the pair of linear equations in general form as:

 

 

Check the cross-multiplication diagram given below:

    

 

Types of questions included in Exercise 3.5 of Pair of Linear Equations in Two Variables:

 

Ex 3.5 Q1: In the first question, you have to find out which of the given pairs of linear equations has a unique solution, no solution, or infinitely many solutions. You have to solve them using the cross-multiplication method if the pair of linear equations has a unique solution. 

 

Ex 3.5 Q2: In this question, you are given pairs of linear equations with some missing values. You have to solve them and find those missing values. You can use the cross-multiplication method to do so. We have provided stepwise solutions to this question in our NCERT Solutions for Class 10 Maths Chapter 3 Ex 3.5. 

 

Ex 3.5 Q3: In this question, you are given a pair of linear equations in two variables. You have to solve it using the substitution method and the cross-multiplication methods. Specific questions like this can be asked in the CBSE board exam as well so you must practice all the algebraic methods thoroughly. 

 

Ex 3.5 Q4: This is an important question of the exercise with 5 subparts. In each subpart, you are given a word problem. You have to formulate a pair of linear equations in two variables by analysing the word problem and then you have to find the solution of those linear equations using the cross-multiplication method. 

Download Free NCERT Solutions for Class 10 Maths Chapter 3 Ex 3.5 

 

You can find the solutions of all four NCERT questions of Ex 3.5 on the askIITians website. Our Maths experts have provided you with easy to understand explanations for all the exercise questions so that you can understand the concept of cross-multiplication. These solutions will act as your guide and will help you master this exercise. 

 

Key features of NCERT Solutions for Class 10 Maths Chapter 3 Ex 3.5 by askIITians:

 

• All the solutions are based on the latest CBSE syllabus and exam pattern. 

• You can study the solutions at your own pace and practice them as many times as you want. 

• You can learn independently with the help of our NCERT Solutions. 

• We have included stepwise explanations and proper reasoning for every exercise question. 

• Referring to our NCERT Solutions will solidify your understanding of the cross-multiplication method. 

 

Download NCERT Solutions for all the other exercises of Chapter 3 Pairs of Linear Equations in Two Variables from the askIITians website: 

 

• 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 3.5 FAQs

 

1. How many solved examples are there in NCERT Class 10 Maths Chapter 3 Ex 3.5? 

There are 3 solved examples and 4 unsolved problems for Ex 3.5 of NCERT Class 10 Maths Chapter 3. The askIITians Maths experts have provided stepwise solutions for all the exercise questions for your practice. 

 

2. How to study Chapter 3 Pairs of Linear Equations of Class 10 Maths? 

askIITians provides a variety of study resources to the students such as revision notes, NCERT Solutions, extra questions, flashcards, daily worksheets and much more. Download them from our website and start practising. 

 

3. I need more help in Class 10 Maths. What should I do? 

Enrol in online coaching by askIITians and learn from our experts. We provide live, interactive classes where students can ask questions, participate in discussions and resolve their doubts. To know more about our online courses, check our website or contact customer support.