CBSE Class 10 Chapter 3 Math NCERT Solutions | Pair of Linear Equations | By Grandmaster Bikram Sutradhar

Pair of Linear Equations SirBikramSutradhar sirbikramsutradhar Class 10 NCERT Solutions

Get CBSE Class 10 Chapter 3 Math NCERT Solutions with step-by-step explanations, graphs, and shortcut tricks. Learn Pair of Linear Equations in Two Variables with substitution, elimination, and graphical methods. Prepared by Grandmaster Bikram Sutradhar for quick learning and exam success!

Grandmaster Bikram Sutradhar presents the best solutions for CBSE Class 10 Chapter 3 – Pair of Linear Equations in Two Variables. This chapter is crucial for board exams, competitive exams, and real-life problem-solving.

✔ Key Highlights:

• Step-by-step solutions for NCERT exercises.
• Graphical representations for better understanding.
• Shortcut tricks to solve quickly.
• Important formulas and tips for exams.

Chapter 3 Overview: Pair of Linear Equations in Two Variables

ax+by+c=0

💡 Key Topics Covered:
✅ Algebraic methods (substitution, elimination, cross-multiplication)
✅ Graphical method
✅ Word problems
✅ Applications in real-life scenarios

NCERT Solutions for Chapter 3 (Exercise-wise)

Exercise 3.1: Introduction to Linear Equations

✔ Understanding consistent and inconsistent equations
✔ Graphical method of solution

📌 Example:
Solve the equations:

1. 2x + 3y = 6
2. 4x – y = 5

✅ Graphical Representation:

Solution:

1. Convert into slope-intercept form
2. Plot points on the graph
3. Find the intersection point

📢 Conclusion: The solution is x = 3, y = 0.

Exercise 3.2: Substitution Method

✔ Step 1: Express one variable in terms of the other.
✔ Step 2: Substitute in the second equation.
✔ Step 3: Solve for both variables.

📌 Example: Solve

1. x + y = 14
2. x – y = 4

Solution:

🔹 Final Answer: (9, 5)

Exercise 3.3: Elimination Method

✔ Add/subtract equations to eliminate one variable.
✔ Solve the remaining equation.
✔ Substitute back to get the second variable.

📌 Example: Solve

1. 3x – 5y = 4
2. 9x = 2y + 7

✅ Graphical Solution & Explanation

Exercise 3.4: Cross Multiplication Method

✔ Formula-based approach
✔ Quick and efficient for large numbers

📌

Exercise 3.5: Word Problems

✔ Real-life applications of linear equations
✔ Step-by-step breakdown

📌 Example:
🚖 Taxi Fare Calculation
Fixed charge = ₹ X, Per km charge = ₹ Y

1. 10 km fare = ₹ 105 → Equation 1
2. 15 km fare = ₹ 155 → Equation 2

✅ Solution using Elimination Method:
X = ₹ 25, Y = ₹ 8 per km

Important Formulas & Tricks for Quick Solutions

📝 Graphical Method: Find intersection points of two lines.
📝 Substitution Method: Express one variable in terms of another.
📝 Elimination Method: Add/subtract equations to eliminate one variable.
📝 Cross Multiplication Method: Use formula for direct solution.

Why Study from Grandmaster Bikram Sutradhar?

⭐ Expert guidance for CBSE & competitive exams
⭐ Unique problem-solving strategies
⭐ Graphical solutions for better understanding
⭐ Shortcut methods to solve in seconds

Frequently Asked Questions (FAQs)

Q1: What is the easiest way to solve linear equations?
✅ The elimination method is often the quickest as it avoids fractions.

Q2: How important is this chapter for board exams?
✅ Very important! At least 5-8 marks in exams come from this topic.

Conclusion

This guide provides detailed NCERT solutions for CBSE Class 10 Chapter 3 – Pair of Linear Equations in Two Variables. By using graphs, shortcuts, and algebraic methods, you can master this chapter easily.

💡 Follow Grandmaster Bikram Sutradhar’s unique approach for 100% success!

📌 Do you want more solved questions or graphs? Let me know in the comments! 👇

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