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Pair of Linear Equations in Two Variables — Syllabus

Telangana Board · Class 10 · Mathematics

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

43 questions30 flashcards9 formulas & key relations5 concepts

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

Topics in Pair of Linear Equations in Two Variables

1

1. Basic Ideas and Definitions

  • A linear equation in two variables has the form ax + by + c = 0, where a² + b² ≠ 0.
  • At least one of a or b must be non-zero, otherwise the equation is not linear in two variables.
  • One equation with two unknowns has many solutions, so two independent equations are needed for a unique solution.
2

2. Formation of Equations from Word Problems

  • Unknown quantities are first identified from the situation, then converted into linear equations.
  • The notebook and pen problem gives the equations 3x + 2y = 80 and 4x + 3y = 110.
  • The cost of a notebook and a pen is found by solving both equations together.
3

3. Graphical Method and Nature of Solutions

  • The graph of each linear equation is a straight line.
  • If two lines intersect, there is one unique solution.
  • If two lines are parallel, there is no solution.
4

4. Algebraic Methods: Substitution and Elimination

  • Substitution works well when one variable is easy to express in terms of the other.
  • Elimination works by making one variable’s coefficients equal and then adding or subtracting the equations.
  • Cross-multiplication is another standard method used in many classes, though the main methods here are substitution and elimination.

Key Concepts

Central concept: Pair of linear equations in two variables and methods of solving them

Unknown quantitiesLinear equation in two variablesPair of linear equationsNeed for two equationsModel methodGraphical methodNature of solutionCoefficient ratio test

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Frequently Asked Questions

What are the important topics in Pair of Linear Equations in Two Variables for Telangana Board Class 10 Mathematics?
Key topics in Pair of Linear Equations in Two Variables include Basic Ideas and Definitions, Formation of Equations from Word Problems, Graphical Method and Nature of Solutions, Algebraic Methods: Substitution and Elimination. Study these first, then practise questions on each for the Telangana Board Class 10 board exam.
How should I revise Pair of Linear Equations in Two Variables for the Telangana Board Class 10 board exam?
Learn the core ideas first, then work through the 43 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 Telangana Board Class 10 Mathematics Syllabus

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