 NCERT Solutions for class 10 Maths Chapter 3 Exercise 3.3 in Hindi and English Medium modified and updated for academic session 2023-24. The solutions of ex. 3.3 class X Maths is revised as per the new textbooks issued for 2023-24 board exams.

• ## Class 10 Maths Exercise 3.3 Solutions

 Class: 10 Mathematics Chapter 3: Exercise 3.3 Content: NCERT Solutions and Study Material Mode of Material: Text, Images and Videos with PDF Session: Academic year 2023-24 Medium: English and Hindi Medium

### NCERT Solutions for class 10 Maths Chapter 3 Exercise 3.3 Ex. 3.3 Class 10 Maths solution Pair of linear equations in two variables in Hindi Medium and English Medium in PDF format. Class 10 CBSE Solutions are available in PDF and Videos Format to download or free to use and study online for session 2023-24.

UP Board students can also take the benefits of these solutions as UP Board, Prayagraj has announced to implement NCERT Books for High School students in the session 2023-24. NCERT Solutions Apps for 2023-24 and PDF Solutions both are updated as per student’s convenience and according to CBSE Curriculum 2023-24 for Gujrat Board, MP Board, UP board / Uttarakhand Board / CBSE board based on new NCERT Books.

### 10 Maths Chapter 3 Exercise 3.3 Solutions

NCERT CBSE Solutions for Class 10 Maths Chapter 3 Exercise 3.3 in English & Hindi medium online to use or download in PDF form free for academic session 2023-24. Download all Exercises of Class 10 Maths Chapter 3 Solutions main page. Download Offline Apps 2023-24 based on latest NCERT Books 2023-24.

#### Important Questions on Linear Equations

1. Two numbers are in the ration of 5:6. If 8 is subtracted from each of the numbers, they become in the ratio of 4:5. Find the numbers. [Answer: 40, 48]
2. Given the linear equation 2x + 3y – 12 = 0, write another linear equation in these variables, such that. geometrical representation of the pair so formed is (i) Parallel Lines (ii) Coincident Lines. [Answer: (i). 4x+6y+10=0, (ii). 4x+6y-24=0]
3. The ratio between girls and boys in a class of 40 students is 2:3. Five new students joined the class. How many of them must be boys so that the ratio between girls and boys becomes 4:5? [Answer: 1]
4. The difference of two number is 66. If one number is four times the other, find the numbers. [Answer: 88, 22]
5. A sum of money was distributed equally among a certain number of children. If there were 10 children more, each would get a rupee less. But if there were 15 children less, each would get of ₹3 more. Find the sum of money distributed and also the number of children. [Answer: ₹200, 40]

### What do you understand about the consistency of lines if the lines intersect in a single point?

If the lines intersect in a single point. Then, the pair of equations has a unique solution (consistent pair of equations).

### What would be the conclusion if the lines are parallel?

If the lines are parallel. In this case, the equations have no solution (inconsistent pair of equations).

### How many solutions are there if the lines are coincident?

If the lines are coincident. In this case, the equations have infinitely many solutions [dependent (consistent) pair of equations]

• For what value of k, the following system of equations will be inconsistent: kx + 3y = k – 3; 12x + ky = k. [Answer: k = -6]
• Solve graphically the pair of linear equations 5x – y = 5 and 3x – 2y = – 4 Also find the co-ordinates of the points where these lines intersect y-axis. [Answer: (2, 5), (0, -5) and (0, 2)]
• A number consists of two digits. When it is divided by the sum of the digits, the quotient is 6 with no remainder. When the number is diminished by 9, the digits are reversed. Find the number. [Answer: 54]
• For what values of a and b the following pair of linear equations have infinite number of solutions?
2x + 3y = 7; a(x + y) – b(x – y) = 3a + b – 2. [Answer: a = 5, b = 1]
• The sum of a two digit number and the number obtained by interchanging the digits is 132. If the two digits differ by 2, find the number. [Answer: 75 or 57]

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### How many questions are there in exercise 3.3 of class 10th mathematics chapter 3?

There are 2 questions in exercise 3.3 of class 10th mathematics chapter 3 (Pair of linear equations in two variables). Q1 contains 4 parts and Q2 contains 5 word problems. Q2 is important.

### How many examples are based on exercise 3.3 of class 10th mathematics?

Only 3 examples (examples 11, 12 and 13) are based on exercise 3.3 (chapter 3 Pair of linear equations in two variables) of class 10th mathematics. All three examples are very important.

### What is the main focus in exercise 3.3 class 10 mathematics?

In exercise 3.3 (chapter 3 Pair of linear equations in two variables) of class 10th mathematics students will learn how to solve pairs of linear equations in two variables by ELIMINATION METHOD.

### What is the method used in exercise 3.3 NCERT 10th Maths?

Elimination Method (stepwise):-
a_1x + b_1y + c_1 = 0
a_2x + b_2y + c_2 = 0
Step 1: First multiply both the equations by some suitable non-zero constants to make the coefficients of one variable (either x or y) numerically equal.
Step 2: Then add or subtract one equation from the other so that one variable gets eliminated. If you get an equation in one variable, go to Step 3. If in Step 2, we obtain a true statement involving no variable, then the original pair of equations has infinitely many solutions. If in Step 2, we obtain a false statement involving no variable, then the original pair of equations has no solution, i.e., it is inconsistent.
Step 3: Solve the equation in one variable (x or y) so obtained to get its value.
Step 4: Substitute this value of x (or y) in either of the original equations to get the value of the other variable.

### Which question is most important in 10th Maths Chapter 3 Exercise 3.3?

Most of the parts of Class 10 Maths Exercise 3.3 Question 2 are asked in CBSE Examination. But the third (iii) part is the most important as it is asked more than twice in Board Examination.

### Is Exercise 3.3 of 10th Maths easy?

Yes, of course it is easy. It need practice only. The exercise 3.3 is quite easy to solve. Students generally face problem to make equations of word problem questions.    Last Edited: August 26, 2023