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Pair of Linear Equations in Two Variables — Syllabus

Karnataka Board · Class 10 · Mathematics

What Pair of Linear Equations in Two Variables covers in Karnataka Board Class 10 Mathematics: 4 topics, for the 2026-27 session.

44 questions20 flashcards4 formulas & key relations5 concepts

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4 Topics · Karnataka Board Class 10 Mathematics · 2026-27

Topics in Pair of Linear Equations in Two Variables

1

Basic Concepts and Definitions

  • A linear equation in two variables x and y has the form ax + by + c = 0, where a, b, c are real numbers and a² + b² ≠ 0
  • A pair of linear equations in two variables consists of two such equations considered together
  • The solution of a pair is the common solution that satisfies both equations simultaneously
2

Types of Solutions Based on Line Relationships

  • Three possible relationships: intersecting lines (unique solution), parallel lines (no solution), coincident lines (infinite solutions)
  • The relationship can be determined by comparing ratios of coefficients
  • Use ratio comparison method: a₁/a₂, b₁/b₂, and c₁/c₂
3

Graphical Method

  • Plot both equations as straight lines on coordinate plane
  • Find intersection point if lines meet
  • Solution is the coordinates of intersection point
4

Substitution Method

  • Express one variable in terms of the other from either equation
  • Substitute this expression into the other equation
  • Solve the resulting single-variable equation

Key Concepts

An equation of the form axThree possibilities existFor equations a₁x + b₁y +Plot both equations as lines onStep 1

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Frequently Asked Questions

What are the important topics in Pair of Linear Equations in Two Variables for Karnataka Board Class 10 Mathematics?
Key topics in Pair of Linear Equations in Two Variables include Basic Concepts and Definitions, Types of Solutions Based on Line Relationships, Graphical Method, Substitution Method. Study these first, then practise questions on each for the Karnataka Board Class 10 board exam.
How should I revise Pair of Linear Equations in Two Variables for the Karnataka Board Class 10 board exam?
Learn the core ideas first, then work through the 44 practice questions on Pair of Linear Equations in Two Variables. Revise definitions regularly and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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All Karnataka Board Class 10 Mathematics Syllabus

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