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Edited By Ramraj Saini | Updated on Nov 13, 2023 03:17 PM IST | #CBSE Class 10th

**NCERT Solutions for class 10 maths ex 3.5 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 3.5 class 10 deals with the cross multiplication method which is one of the methods to solve the pair of linear equations. In exercise 3.5 Class 10 Maths, pair of linear equations can also be solved by many non-graphical methods such as elimination method, substitution method and cross multiplication method but the NCERT book Class 10 Maths chapter 3 exercise 3.5 focuses on solving the equations only by cross multiplication method it is the easiest and straight forward method.

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This Story also Contains

- NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.5
- Download Free Pdf of NCERT Solutions for Class 10 Maths chapter 3 exercise 3.5
- Assess NCERT Solutions for Class 10 Maths chapter 3 exercise 3.5
- More About NCERT Solutions for Class 10 Maths Exercise 3.5
- Benefits of NCERT Solutions for Class 10 Maths Exercise 3.5
- NCERT Solutions of Class 10 Subject Wise
- Subject Wise NCERT Exemplar Solutions

These class 10 maths ex 3.5 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 3.6
- Pair of Linear Equations in two variables Exercise 3.7

**Pair of Linear Equations in Two Variables Class 10 Chapter 3 Excercise: 3.5**

Answer:

Given, two equations,

Comparing these equations with , we get

As we can see,

Hence, the pair of equations has no solution.

Answer:

Given, two equations,

Comparing these equations with , we get

As we can see,

Hence, the pair of equations has exactly one solution.

By Cross multiplication method,

Answer:

Comparing these equations with , we get

As we can see,

Hence, the pair of equations has infinitely many solutions.

Answer:

Given the equations,

Comparing these equations with , we get

As we can see,

Hence, the pair of equations has exactly one solution.

By Cross multiplication method,

Answer:

Given equations,

As we know, the condition for equations to have an infinite solution is

So, Comparing these equations with, , we get

From here we get,

Also,

Now, Subtracting (2) from (1) we get

Substituting this value in (1)

Hence, .

Q2 (ii) For which value of k will the following pair of linear equations have no solution?

Answer:

Given, the equations,

As we know, the condition for equations to have no solution is

So, Comparing these equations with, , we get

From here we get,

Hence, the value of K is 2.

Q3 Solve the following pair of linear equations by the substitution and cross-multiplication methods :

Answer:

Given the equations

By Substitution Method,

From (1) we have

Substituting this in (2),

Substituting this in (3)

Hence .

By Cross Multiplication Method

Answer:

Let the fixed charge be x and the cost of food per day is y,

Now, According to the question

Also

Now subtracting (1) from (2),

Putting this value in (1)

Hence, the Fixed charge is Rs 400 and the cost of food per day is Rs 30.

Answer:

Let numerator of a fraction be x and the denominator is y.

Now, According to the question,

Also,

Now, Subtracting (1) from (2) we get,

Putting this value in (2) we get,

Hence, the fraction is

.

Answer:

Let the number of right answer and wrong answer be x and y respectively

Now, According to the question,

And

Now, subtracting (2) from (1) we get,

Putting this value in (1)

Hence the total number of question is

Answer:

Let the speed of the first car is x and the speed of the second car is y.

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

the relative speed when they are going in the same direction= x - y

the relative speed when they are going in the opposite direction= x + y

The given relative distance between them = 100 km.

Now, As we know,

Relative distance = Relative speed * time .

So, According to the question,

Also,

Now Adding (1) and (2) we get

putting this in (1)

Hence the speeds of the cars are 40 km/hour and 60 km/hour.

Answer:

Let be the length of the rectangle and be the width,

Now, According to the question,

Also,

By Cross multiplication method,

Hence the length and width of the rectangle are 17 units and 9 units respectively.

Class 10 Maths chapter 3 exercise 3.5: The questions in exercise 3.5 Class 10 Maths, broadly consist of four types of questions. In question one we have to identify whether the pair of equations has a unique solution, no solution, or infinitely many solutions. In question two we have to find the extra variable a and b they can be found with the help of the condition which is applied to the question of equation three is a direct question in which we have to solve both substitution method and cross multiplication method. in question four there are word problems based on real-life application. Also students can get access of Pair of linear equations in two variables notes to revise all the concepts discussed in this chapter.

- Chapter 3 exercise 3.5 in Class 10 Maths includes a wide range of problems regarding solving a pair of linear equations using the cross multiplication approach.
- NCERT Class 10 Maths chapter 3 exercise 3.5, will be helpful in solving NCERT Class 11 chapter 6- linear inequalities
**Exercise 3.5 in Class 10 Maths**involves calculating a pair of linear equations using a non-graphical approach, namely the cross multiplication method, which is a key idea in the chapter.

**Also see-**

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

1. How many ways are there to solve a pair of linear equations with two variables according to NCERT solutions for Class 10 Maths 1 exercise 3.5 ?

Graphical method

Algebraic method

2. How many types of algebraic methods are there to solve a pair of linear equations with two variables according to NCERT solutions for Class 10 Maths 1 exercise 3.5 ?

According to NCERT solutions for Class 10 Maths 1 exercise 3.5 there are three ways to solve a pair of linear equations with a single variable by the algebraic method.

3. Name all the types of algebraic methods to solve a pair of linear equations with two variables according to NCERT solutions for Class 10 Maths 1 exercise 3.5 ?

Substitution method

Elimination method

Cross-multiplication Method

4. Sometimes we can get the statement with no variable. What does that mean ?

Statement with no variable means all the values for that variable is true we can say this when the variable itself get eliminated from the equation leaving the same constant at both sides

5. What is the type of linear equation when we get a statement with no variable?

The pair of linear equations can be said to have an infinite number of solutions.

6. When we have defined the value for both the variables, what is the type of linear equation ?

We might remark that the solutions to the pair of linear equations are inconsistent.

7. What is the total number of solved examples based on the cross multiplication method prior to Exercise 3.5 Class 10 Maths?

There are mainly 3 questions that are solved before the Class 10 Maths chapter 3 exercise 3.5

8. How many questions are there in the Exercise 3.5 Class 10 Maths?

There are 4 questions and question 1 has 4 subparts, question 2 has 2 subparts and question 4 has 5 subparts.

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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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