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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 questions20 flashcards5 concepts

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4 Topics · Gujarat Board Class 10 Mathematics

Topics in Pair of Linear Equations in Two Variables

1

Introduction and Basic Concepts

  • A linear equation in two variables x and y has the general form ax + by + c = 0, where a, b, c are real numbers and a² + b² ≠ 0
  • A pair of linear equations consists of two such equations that need to be solved simultaneously
  • Real-life situations often lead to pairs of linear equations, like cost problems, age problems, speed-time problems
2

Graphical Method of Solution

  • Each linear equation represents a straight line when plotted on a coordinate plane
  • The solution of the pair is the point of intersection of the two lines (if they intersect)
  • Three possible cases: lines intersect at one point, lines are parallel, or lines coincide
3

Nature of Solutions Based on Coefficients

  • For equations a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0:
  • If a₁/a₂ ≠ b₁/b₂, then unique solution (intersecting lines)
  • If a₁/a₂ = b₁/b₂ = c₁/c₂, then infinitely many solutions (coincident lines)
4

Substitution Method

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

Key Concepts

An equation of the form axTwo linear equations considered togetherPlot both equations as lines onSolve one equation for one variableMultiply equations by suitable constants

Frequently Asked Questions

What are the important topics in Pair of Linear Equations in Two Variables for Gujarat Board Class 10 Mathematics?
Pair of Linear Equations in Two Variables covers several key topics that are frequently asked in Gujarat Board Class 10 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
How to score full marks in Pair of Linear Equations in Two Variables — Gujarat Board Class 10 Mathematics?
Start by understanding all key concepts. Practise previous year questions from this chapter. Revise formulas and definitions regularly. Use flashcards for quick revision 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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