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Edited By Ramraj Saini | Updated on Nov 13, 2023 03:23 PM IST | #CBSE Class 10th

**NCERT Solutions for class 10 maths ex 3.6 Pair of Linear Equations in two variables** is discussed here. These NCERT solutions are created by subject matter expert at Careers360 considering the **latest syllabus and pattern of CBSE 2023-24**. This ex 3.6 class 10 consists of two questions, each with subparts. The first is straightforward, requiring only direct substitutions of the mathematical formula, whereas the second involves word problems. In this exercise, the majority of the variables are in fractional form, meaning that they are nonlinear, since the variables are now infraction, we can’t take the value of the denominator as zero because it will be against the definition of the fraction.

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This Story also Contains

- NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.6
- Download Free Pdf of NCERT Solutions for Class 10 Maths chapter 3 exercise 3.6
- Assess NCERT Solutions for Class 10 Maths chapter 3 exercise 3.6
- More About Ncert Solutions For Class 10 Maths Exercise 3.6
- Benefits of NCERT Solutions for Class 10 Maths Exercise 3.6
- NCERT Solutions of Class 10 Subject Wise
- Subject Wise NCERT Exemplar Solutions

These **class 10 maths ex 3.6 solutions** are designed as per the students demand covering comprehensive, step by step solutions of every problem. Practice these questions and answers to command the concepts, boost confidence and in depth understanding of concepts. Students can find all exercise together using the link provided below.

- Pair of Linear Equations in Two Variables Exercise 3.1
- Pair of Linear Equations in Two Variables Exercise 3.2
- Pair of Linear Equations in Two Variables Exercise 3.3
- Pair of Linear Equations in Two Variables Exercise 3.4
- Pair of Linear Equations in Two Variables Exercise 3.5
- Pair of Linear Equations in Two Variables Exercise 3.7

**Pair of Linear Equations in Two Variables Class 10 Chapter 3 Excercise: 3.6**

Q1(i) Solve the following pairs of equations by reducing them to a pair of linear equations:

Answer:

Given Equations,

Let,

Now, our equation becomes

And

By Cross Multiplication method,

And Hence,

Q1(ii) Solve the following pairs of equations by reducing them to a pair of linear equations:

Answer:

Given Equations,

Let,

Now, our equation becomes

And

By Cross Multiplication method,

So,

.

And hence

Q1(iii) Solve the following pairs of equations by reducing them to a pair of linear equations:

Answer:

Given Equations,

Let,

Now, our equation becomes

And

By Cross Multiplication method,

And Hence,

Q1(iv) Solve the following pairs of equations by reducing them to a pair of linear equations:

Answer:

Given Equations,

Let,

Now, our equation becomes

And

Multiplying (1) by 3 we get

Now, adding (2) and (3) we get

Putting this in (2)

Now,

Hence,

Q1(v) Solve the following pairs of equations by reducing them to a pair of linear equations:

Answer:

Given Equations,

Let,

Now, our equation becomes

And

By Cross Multiplication method,

And Hence,

Q1(vi) Solve the following pairs of equations by reducing them to a pair of linear equations:

Answer:

Given Equations,

Let,

Now, our equation becomes

And

By Cross Multiplication method,

And Hence,

Q1(vii) Solve the following pairs of equations by reducing them to a pair of linear equations:

Answer:

Given Equations,

Let,

Now, our equation becomes

And

By Cross Multiplication method,

Now,

And,

Adding (3) and (4) we get,

Putting this value in (3) we get,

And Hence,

Q1(viii) Solve the following pairs of equations by reducing them to a pair of linear equations:

Answer:

Given Equations,

Let,

Now, our equation becomes

And

Now, Adding (1) and (2), we get

Putting this value in (1)

Now,

And

Now, Adding (3) and (4), we get

Putting this value in (3),

Hence,

Answer:

Let the speed of Ritu in still water be x and speed of current be y,

Let's solve this problem by using relative motion concept,

the relative speed when they are going in the same direction (downstream)= x +y

the relative speed when they are going in the opposite direction (upstream)= x - y

Now, As we know,

Relative distance = Relative speed * time .

So, According to the question,

And,

Now, Adding (1) and (2), we get

Putting this in (2)

Hence,

Hence Speed of Ritu in still water is 6 km/hour and the speed of the current is 4 km/hour

Answer:

Let the number of days taken by woman and man be x and y respectively,

The proportion of Work done by a woman in a single day

The proportion of Work done by a man in a single day

Now, According to the question,

Also,

Let,

Now, our equation becomes

And

By Cross Multiplication method,

So,

Answer:

Let the speed of the train and bus be u and v respectively

Now According to the question,

And

Let,

Now, our equation becomes

And

By Cross Multiplication method,

And Hence,

Hence the speed of the train and bus are 60 km/hour and 80 km/hour respectively.

NCERT solutions for Class 10 Maths exercise 3.6- consists of two extremely important questions. In order to answer the first question, you must reduce the pair of equations to a pair of linear equations. Students must express problems as a pair of equations in order to determine their answers to the second question. Furthermore, exercise 3.6 is a more advanced chapter exercise. Above all, this task is an excellent technique to assess a student's ability to solve linear equations in two variables. Also students can get access of Pair of linear equations in two variables notes to revise all the concepts discussed in this chapter.

- NCERT book
**Exercise 3.6 Class 10 Math**s, is based on the basic idea of solving a pair of equations with fractional variables. - NCERT solutions for Class 10 Maths chapter 3 exercise 3.6 helps to solve complex non-linear equations by simplifying it to simple linear equations.
- If you go through the NCERT solution for Class 10 Maths chapter 3 exercise 3.6, we can see that we will have to use the previous solving methods like substitution and elimination. Thus, this part helps us to clear our previous concepts too.

**Also see-**

As per latest 2024 syllabus. Maths formulas, equations, & theorems of class 11 & 12th chapters

1. What are the methods used for solving linear equation in two variables?

We use substitution method, graphical and elimination method etc.

2. Which one of the methods is easier compared to the other between Graphical and Elimination Method?

Because it is time-efficient and does not take a long time to complete. Hence, the elimination method is preferred.

3. What is the basic concept behind NCERT solutions for Class 10 Maths 3 exercise 3.4?

In this exercise, the majority of the variables are in fractional form, meaning that they are nonlinear, since the variables are now infractions, we can’t take the value of the denominator as zero because it will be against the definition of the fraction.

4. How do we solve the majority of the variables which are in fractional form?

We substitute the fraction variable as another new variable; thus, we get two new linear equations that we can solve easily.

5. Is there a role for substitution in the elimination method?

Yes, we can get the value of the second equation by substituting the value of the first variable into any of the equations.

6. Do we need any kind of substitution in order to get the final answer?

Yes, we need substitution in order to get the final answer.

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6 minHave a question related to CBSE Class 10th ?

Hello

The Sadhu Ashram in Aligarh is located in Chhalesar . The ashram is open every day of the week, except for Thursdays . On Mondays, Wednesdays, and Saturdays, it's open from 8:00 a.m. to 7:30 p.m., while on Tuesdays and Fridays, it's open from 7:30 a.m. to 7:30 p.m. and 7:30 a.m. to 6:00 a.m., respectively . Sundays have varying hours from 7:00 a.m. to 8:30 p.m. . You can find it at Chhalesar, Aligarh - 202127 .

Hello Aspirant, Hope your doing great, your question was incomplete and regarding what exam your asking.

Yes, scoring above 80% in ICSE Class 10 exams typically meets the requirements to get into the Commerce stream in Class 11th under the CBSE board . Admission criteria can vary between schools, so it is advisable to check the specific requirements of the intended CBSE school. Generally, a good academic record with a score above 80% in ICSE 10th result is considered strong for such transitions.

hello Zaid,

Yes, you can apply for 12th grade as a private candidate .You will need to follow the registration process and fulfill the eligibility criteria set by CBSE for private candidates.If you haven't given the 11th grade exam ,you would be able to appear for the 12th exam directly without having passed 11th grade. you will need to give certain tests in the school you are getting addmission to prove your eligibilty.

best of luck!

According to cbse norms candidates who have completed class 10th, class 11th, have a gap year or have failed class 12th can appear for admission in 12th class.for admission in cbse board you need to clear your 11th class first and you must have studied from CBSE board or any other recognized and equivalent board/school.

You are not eligible for cbse board but you can still do 12th from nios which allow candidates to take admission in 12th class as a private student without completing 11th.

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