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Pair of Linear Equations in Two Variables

Gujarat Board · Class 10 · Mathematics

Complete topic list for Pair of Linear Equations in Two Variables in Gujarat Board Class 10 Mathematics. Key concepts, sub-topics, and what to focus on for board exams.

45 questions25 flashcards5 concepts

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4 Topics · Gujarat Board Class 10 Mathematics

Topics in Pair of Linear Equations in Two Variables

1

Basic Concepts and Definitions

  • A linear equation in two variables has the general form: ax + by + c = 0, where a, b, c are real numbers and a ≠ 0, b ≠ 0.
  • A pair of linear equations in two variables consists of TWO such equations considered together.
  • The general form of a pair of linear equations is: a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0.
2

Graphical Method and Nature of Solutions

  • The graphical method involves plotting both lines on the same coordinate plane and observing their relationship.
  • CASE 1 – Intersecting Lines: The two lines meet at exactly ONE point. This point is the unique solution. The pair is CONSISTENT.
  • CASE 2 – Coincident Lines: The two lines overlap completely. Every point on the line is a solution — INFINITELY MANY solutions. The pair is DEPENDENT and CONSISTENT.
3

Substitution Method

  • In this method, you express one variable in terms of the other from one equation, and substitute into the second equation.
  • This converts the pair of equations into a SINGLE equation in one variable, which is easy to solve.
  • The substitution method works well when one of the coefficients is 1 (making it easy to isolate a variable).
4

Elimination Method

  • In this method, you add or subtract the two equations to ELIMINATE one variable, then solve for the remaining one.
  • If the coefficients of one variable are the same (or negatives of each other), that variable can be directly eliminated by adding or subtracting.
  • If the coefficients are different, MULTIPLY one or both equations by suitable constants to make the coefficients of one variable equal.

Key Concepts

A linear equation in two variablesA pair of linear equationsA pair of linear equationsTwo linear equations are INDEPENDENT ifThe graphical method involves plotting both

Frequently Asked Questions

What are the important topics in Pair of Linear Equations in Two Variables for Gujarat Board Class 10 Mathematics?
Key topics in Pair of Linear Equations in Two Variables include Pair of Linear Equations — Complete Chapter Overview, Decision Tree: Which Method to Use for Solving Linear Equations, Chapter Overview: Pair of Linear Equations in Two Variables. These are the concepts Gujarat Board Class 10 examiners draw on most — study them first, then practise related questions.
How to score full marks in Pair of Linear Equations in Two Variables — Gujarat Board Class 10 Mathematics?
Understand the core concepts first, then work through the 45 practice questions available for this chapter. Revise formulas and 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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