NCERT Solutions for Class 10 Maths Chapter 3 – Pair of Linear Equations in Two Variables Exercise 3.4

NCERT Solutions for Class 10 Maths Chapter 3 – Pair of Linear Equations in Two Variables Exercise 3.4 are designed to provide a clear understanding of solving linear equations using the elimination method, substitution method, and graphical method. This exercise delves into real-world applications, helping students grasp how to apply these methods to solve practical problems in mathematics.

Exercise 3.4 focuses on solving word problems involving pairs of linear equations in two variables, allowing students to apply their knowledge of algebra to everyday situations. The solutions are presented in a step-by-step manner, ensuring that students understand the correct approach to formulating and solving equations based on given conditions.

NCERT Solutions for Class 10 Maths Chapter 3 – Pair of Linear Equations in Two Variables Exercise 3.4

Pair of Linear Equations in Two Variables

Medium

Q.

Solve 2x + 3y = 11 and 2x − 4y = −24 and hence find the value of 'm' for which y = mx + 3.

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Pair of Linear Equations in Two Variables

Medium

Q.

Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method:
(i)   If we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces to 1. It becomes ½ if we only add 1 to the denominator. What is the fraction?

(ii)  Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu?

(iii) The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.

(iv) Meena went to a bank to withdraw ₹ 2000. She asked the cashier to give her ₹50 and  ₹100 notes only. Meena got 25 notes in all. Find how many notes of ₹ 50 and  ₹100 she received.

(v) A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid ₹ 27 for a book kept for seven days, while Susy paid ₹ 21 for the book she kept for five days. Find the fixed charge and the charge for each extra day.

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Pair of Linear Equations in Two Variables

Medium

Q.

$\begin{array}{l}\text{Solve the following pair of linear equations by the}\\ \text{substitution and cross-multiplication methods:}\\ 8\mathrm{x}+5\mathrm{y}=9\\ 3\mathrm{x}+2\mathrm{y}=4\end{array}$

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Pair of Linear Equations in Two Variables

Medium

Q.

$\begin{array}{l}\text{Form the pair of linear equations in the following}\\ \text{problems and find their solutions (if they exist)}\\ \text{by any algebraic method:}\\ \text{ (i) A part of monthly hostel charges is fixed and the}\\ \text{ remaining depends on the number of days one}\\ \text{ has taken food in the mess. When a student A}\\ \text{ takes food for 20 days she has to pay }₹\text{1000}\\ \text{ as hostel charges whereas a student B, who}\\ \text{ takes food for 26 days, pays }₹\text{1180 as hostel}\\ \text{ charges. Find the fixed charges and the cost of }\\ \text{ food per day.}\\ \text{(ii) A fraction becomes }\frac{1}{3}\text{ when 1 is subtracted from }\\ \text{ the numerator and it becomes }\frac{1}{4}\text{ when 8 is added}\\ \text{ to its denominator. Find the fraction.}\\ \text{(iii) Yash scored 40 marks in a test, getting 3 marks}\\ \text{ for each right answer and losing 1 mark for each}\\ \text{ wrong answer. Had 4 marks been awarded for}\\ \text{ each correct answer and 2 marks been deducted}\\ \text{ for each incorrect answer, then Yash would have}\\ \text{ scored 50 marks. How many questions were there}\\ \text{ in the test?}\end{array}$
$\begin{array}{l}\text{(iv) Places A and B are 100 km apart on a highway. One}\\ \text{ car starts from A and another from B at the same}\\ \text{ time. If the cars travel in the same direction at}\\ \text{ different speeds, they meet in 5 hours. If they}\\ \text{ travel towards each other, they meet in 1 hour.}\\ \text{ What are the speeds of the two cars?}\\ \text{(v) The area of a rectangle gets reduced by 9 square}\\ \text{ units, if its length is reduced by 5 units and}\\ \text{ breadth is increased by 3 units. If we increase}\\ \text{ the length by 3 units and the breadth by 2 units},\\ \text{ the area increases by 67 square units}.\text{ Find the}\\ \text{ dimensions of the rectangle.}\end{array}$

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Pair of Linear Equations in Two Variables

Medium

Q.

Solve the following system of linear equations 7x – 2y = 5 and 8x + 7y = 15 and verify your answer.

[CBSE - 2024]

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These solutions are aligned with the latest CBSE syllabus, providing detailed explanations and methodical steps for solving problems and enhancing exam preparation.

Q1: Solve 2x + 3y = 11 and 2x − 4y = −24 and hence find the value of 'm' for which y = mx + 3.

Solution:

1. The given equations are:

   • 2x + 3y = 11

   • 2x − 4y = −24

   Solve this system of linear equations using either substitution or elimination.

   By solving, you will find the values of x and y. Once you have those, substitute them into the equation y = mx + 3 to determine the value of m.

View Solution for Q1

Q2: Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method:

1. If we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces to 1. It becomes ½ if we only add 1 to the denominator. What is the fraction?

2. Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu?

3. The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.

4. Meena went to a bank to withdraw ₹ 2000. She asked the cashier to give her ₹50 and ₹100 notes only. Meena got 25 notes in all. Find how many notes of ₹ 50 and ₹ 100 she received.

5. A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid ₹ 27 for a book kept for seven days, while Susy paid ₹ 21 for the book she kept for five days. Find the fixed charge and the charge for each extra day.

Solution:

• For each of these word problems, form a pair of linear equations based on the given conditions and solve using the elimination method.

View Solution for Q2

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

• 8x + 5y = 9

• 3x + 2y = 4

Solution:

• You can solve this system using substitution or the cross-multiplication method. First, solve for x or y in one of the equations and substitute into the other equation to find the value of the second variable.

View Solution for Q3

Q4: Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method:

1. A part of monthly hostel charges is fixed, and the remaining depends on the number of days one has taken food in the mess. When student A takes food for 20 days, she has to pay ₹1000 as hostel charges, whereas student B, who takes food for 26 days, pays ₹1180. Find the fixed charges and the cost of food per day.

2. A fraction becomes 1/3 when 1 is subtracted from the numerator and it becomes 1/4 when 8 is added to its denominator. Find the fraction.

3. Yash scored 40 marks in a test, getting 3 marks for each right answer and losing 1 mark for each wrong answer. Had 4 marks been awarded for each correct answer and 2 marks been deducted for each incorrect answer, then Yash would have scored 50 marks. How many questions were there in the test?

4. Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars?

5. The area of a rectangle gets reduced by 9 square units, if its length is reduced by 5 units and its breadth is increased by 3 units. If we increase the length by 3 units and the breadth by 2 units, the area increases by 67 square units. Find the dimensions of the rectangle.

Solution:

• For each problem, form the linear equations based on the given conditions and solve them algebraically.

View Solution for Q4

FAQs: Class 10 Maths Chapter 3 – Exercise 3.4

Q1. What is the focus of Exercise 3.4?
Answer:
Exercise 3.4 focuses on solving word problems involving linear equations in two variables, where students need to set up equations based on the information provided and then solve them using algebraic methods.

Q2. How do I solve word problems in this exercise?
Answer:
To solve word problems, follow these steps:

1. Read the problem carefully and identify the given information.

2. Translate the problem into a pair of linear equations in two variables.

3. Use the elimination or substitution method to solve the equations.

4. Verify your answer by checking the values in the original equations.

Q3. How do I form equations from a word problem?
Answer:
Identify the two unknowns (variables), create two relationships between them, and translate these relationships into algebraic expressions. These expressions will form your linear equations.

Q4. Are there any special tips for solving word problems?
Answer:

• Read carefully and identify what each variable represents.

• Set up equations step-by-step, based on the relationships mentioned in the problem.

• Use substitution or elimination methods to solve the equations.

Q5. How do NCERT Solutions help with exam preparation?
Answer:
These solutions provide step-by-step explanations to help students learn how to solve word problems systematically. By practicing these problems, students can improve their problem-solving skills and prepare efficiently for exams.