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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Full Stack Developer and 5-Time World Record Holder, Grandmaster Bikram Sutradhar

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