The RD Sharma Class 10 Solutions 2025-26 for Pair of Linear Equations in Two Variables is an important part of the RD Sharma Class 10 Chapter 3 Solutions and the CBSE Class 10 syllabus. This topic helps students learn how to solve equations with two variables like x and y using easy methods such as substitution and elimination.
Many students use both RD Sharma Class 10 Pair of Linear Equations in Two Variables and NCERT Solutions for Class 10 Maths to better understand concepts and prepare for exams. The detailed step-by-step solutions in RD Sharma Solutions make learning simple and clear. You can also download the RD Sharma Class 10 Pair of Linear Equations in Two Variables PDF to study anytime. This chapter builds strong problem-solving skills which are very useful for exams and higher-level maths.
RD Sharma Class 10 Solutions 2025-26 for this chapter is a great tool to help you master the concepts, improve your confidence, and score better marks in Class 10 Maths.
RD Sharma Class 10 Chapter 3 Pair of Linear Equations in Two Variables PDF with Solutions
If you are a student of Class 10, then RD Sharma Class 10 Solutions 2025-26 PDF is very helpful for you. Specially for Pair of Linear Equations in Two Variables chapter. This is from RD Sharma Class 10 Chapter 3 which is very important part of CBSE Class 10 Syllabus. Many students also study NCERT Solutions for Class 10 but RD Sharma Class 10 Pair of Linear Equations in Two Variables PDF helps more with extra practice.
This chapter explains how to solve two variables questions easily by different methods. With RD Sharma Class 10 Solutions 2025-26 PDF, you can download and practice step by step questions. This is also matching latest CBSE Class 10 syllabus.
Important Question for RD Sharma Class 10 - Chapter 3 - Pair of Linear Equations in Two Variables
Ques: Akhila went to a fair. The number of times she played Hoopla is half the number of rides on the giant wheel. Each ride costs ₹3, and each Hoopla costs ₹4. If she spent ₹20 in total, represent this situation algebraically and graphically.
Solution: Let number of rides = x, number of times Hoopla = y
- y = ½x → x - 2y = 0
- 3x + 4y = 20
This forms a pair of equations.
Ques: A father is three times as old as his son. After twelve years, his age will be twice that of his son. Find their present ages.
Solution: Let father's age = x, son's age = y
- x = 3y
- x + 12 = 2(y + 12) → x - 2y = 12
- Solving: x = 36, y = 12 (Father is 36 years, son is 12 years old).
Ques: Solve graphically
x + y = 3
2x + 5y = 12
Solution: Plotting both equations, intersection gives solution x = 1, y = 2.
Ques: The sum of a number and twice its reciprocal is 10. Represent as a pair of linear equations and solve it.
Solution: Let the number be x, its reciprocal is y (= 1/x):
x + 2y = 10, xy = 1 → y = 1/x
This can be solved by substitution or elimination.
Ques: The sum of a two-digit number and the number obtained by reversing its digits is 99. The digits differ by 3. Find the number.
Solution: Let tens = x, units = y.
(xy + yx = 99), (|x - y| = 3).
Representation and solution give possible values: e.g., 63 and 36.
Ques: Solve
x – 2y = 5
2x + 3y = 10
Solution:
By substitution
From first, x = 5 + 2y
Plug in second:
2(5 + 2y) + 3y = 10 ⇒ 10 + 4y + 3y = 10 ⇒ 7y = 0 ⇒ y = 0
Thus, x = 5, y = 0.
Ques: Solve by cross-multiplication:
x + 2y + 1 = 0
2x – 3y – 12 = 0
Solution: The solution is x = 3, y = –2.
Ques: Solve
3x + 2y + 25 = 0
2x + y + 10 = 0
Solution:
The solution is x = 5, y = –20.
Ques: Solve for x and y
2x + y = 35
3x + 4y = 65
Solution: The solution is x = 5, y = 25.
Ques: The sum of the numerator and denominator of a fraction is 8. If the denominator is increased by 2, numerator decreased by 2, the fraction becomes 1/2. Find the fraction.
Solution: Let num = x, denom = y
x + y = 8
(x – 2)/(y + 2) = 1/2
By cross-multiplication:
2(x – 2) = y + 2
2x – 4 = y + 2
2x – y = 6
Solving, x = 7, y = 1 (fraction = 7/1).
Ques: Find the value of k such that the system has infinitely many solutions:
2x + 3y = 2
(k + 2)x + (2k + 1)y = 2(k – 1)
Solution: k = 4.
Ques: Solve
0.4x + 0.3y = 1.7
0.7x – 0.2y = 0.8
Solution: x = 2, y = 3.
Ques: Solve
x/2 + y = 0.8
7/(x + y/2) = 10
Solution: x = 2/5, y = 3/5.
Ques: Solve using substitution
x/7 + y/3 = 5
x/2 – y/9 = 6
Solution: x = 14, y = 9.
Ques: Represent and solve
x + 2y = 3/2
2x + y = 3/2
Solution: x = 1/2, y = 1/2.
Ques: If 1/(7x) + 1/(6y) = 3, 1/(2x) – 1/(3y) = 5. Solve for x and y.
Solution: x = 1/14, y = 1/6.
Ques: Solve
x + y = 6
x – y = 2
Solution: Add: 2x = 8 ⇒ x = 4; y = 2.
Ques: 3x – 4y – 1 = 0
2x – (8/3)y + 5 = 0
Solution: x = 1, y = 1.
Ques: Find the solution set for
2/x + 5/y = 1
60/x + 40/y = 19
Solution:
x = 4, y = 10
Ques: If (x + y)/xy = 2 and (x – y)/xy = 6, solve for x and y.
Solution: From the two equations,
x = –1/2, y = 1/4.
RD Sharma Solutions Class 10 Chapter 3 - Pair of Linear Equations in Two Variables PDF Overview
The RD Sharma Solutions Class 10 Chapter 3 PDF helps students learn maths easily and quickly. This chapter, called Pair of Linear Equations in Two Variables, is very important in algebra and is part of the latest CBSE Class 10 syllabus. It teaches how to solve equations with two variables like x and y, which is useful for exams and future studies.
Main topics in Chapter 3:
- Understanding linear equations in two variables
- Methods to solve them: substitution, elimination, and cross multiplication
- Graphical representation of linear equations
- Types of solutions: unique, infinite, or no solution
- Applications of pair of linear equations in daily problems
The RD Sharma Class 10 Chapter 3 PDF provides easy step-by-step solutions, simple explanations, and helpful hints for all questions. It is perfect for practice and revision at home. Sometimes students feel this chapter is tough, but the detailed solutions in the PDF make it simple to understand and solve problems.
Why use RD Sharma Solutions Class 10 Chapter 3 PDF?
- Every question is solved in a clear and simple way
- Useful for homework, tests, and exam preparation
- Important formulas and concepts are explained with examples
- You can download the PDF and study without internet
- Free access and helpful even if you make mistakes while practicing
Advantages of Solving RD Sharma Class 10 Chapter 3 - Pair of Linear Equations in Two Variables
- Builds strong concepts: Helps you understand solving two-variable equations and their graphs, which is needed for higher maths too.
- Improves problem-solving: Includes many practice problems to boost thinking skills and accuracy.
- Board exam ready: Questions follow the latest CBSE Class 10 syllabus to prepare you well for board exams.
- Increases speed and accuracy: Regular practice with this PDF improves how fast and correctly you solve questions during exams.
- Full solutions: Detailed answers explain each step clearly, so you don’t get stuck anywhere.
- Prepares for competitive exams: This chapter is important for exams like JEE and NEET, so practicing here builds a strong base.
Frequently Asked Questions
This chapter covers solving linear equations with two variables, methods like substitution, elimination, and cross multiplication, graphical representation, types of solutions, and real-life applications of these equations.
The PDF provides step-by-step solutions and clear explanations for all questions based on the latest CBSE Class 10 syllabus, helping you practice effectively for board exams and improve accuracy and speed.
Yes, the solutions are written in simple language with detailed steps, making it easier for students who find algebra or two-variable equations difficult to understand and solve problems confidently.
Definitely! Understanding and practicing pair of linear equations is important for exams like JEE and NEET, so these solutions help build a strong foundation for competitive exams.
Yes, you can download the PDF and study offline anytime. This makes it convenient for students to practice without needing internet access.