Class 10 CBSE Maths Chapter 3: Pair of Linear Equations – Full Notes, Formulas & PDF

 Chapter 3: Pair of Linear Equations in Two Variables – Class 10 CBSE Maths

In this chapter, we learn how to form and solve two linear equations in two variables. It is an important chapter for Class 10 Board Exams and helps build the foundation for Algebra in higher studies.

✏️ What is a Linear Equation in Two Variables?

An equation of the form ax + by + c = 0, where a, b, and c are real numbers, and x and y are variables, is called a linear equation in two variables.

Example:
2x + 3y = 6
x − y = 4

📈 Graphical Method to Solve Equations

  • Plot both equations on the graph.

  • The point of intersection is the solution.

  • If the lines intersect → One solution

  • If the lines are parallel → No solution

  • If the lines overlap → Infinite solutions

✍️ Algebraic Methods of Solving Equations

  1. 🔁 Substitution Method

  2. ➖ Elimination Method

  3. ✳️ Cross Multiplication Method

🔢 Important Formulas

✅ General Form: ax + by + c = 0
✅ Cross Multiplication Formula:

x / (b1c2 − b2c1) = y / (c1a2 − c2a1) = 1 / (a1b2 − a2b1)

Where:
Equation 1: a₁x + b₁y + c₁ = 0
Equation 2: a₂x + b₂y + c₂ = 0

💡 Applications of Linear Equations

  • Solving age-related problems

  • Mixture and solution problems

  • Time-speed-distance problems

  • Business profit-loss questions

📥 Download Chapter 3 PDF Notes

👉 Click here to download the full PDF notes for Chapter 3

The PDF includes:

📥 Download Chapter 3 PDF Notes

👉 Click below to download the complete PDF notes with formulas, examples, and explanations:

👉 Download Chapter 3 – Pair of Linear Equations in Two Variables PDF

  • Complete explanations

  • Step-by-step solved problems

  • All methods and formulas

  • Practice questions

🔗 Read Other Chapters

📘 Chapter 1: Real Numbers
📗 Chapter 2: Polynomials
📙 Chapter 4: Quadratic Equations (Coming Soon)

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