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Linear Equations in Two Variables

Gujarat Board · Class 9 · Mathematics

Quick revision notes for Linear Equations in Two Variables — Gujarat Board Class 9 Mathematics. Key concepts, formulas, and definitions for last-minute revision.

45 questions24 flashcards5 concepts

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An infographic defining a linear equation in two variables, showing its general form (Ax + By + C = 0) and examples, with labels for variables and coefficients.
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Key Topics to Revise

1

What is a Linear Equation in Two Variables?

  • A linear equation in two variables contains exactly two variables, usually x and y.
  • The standard form is ax + by + c = 0, where a and b are not both zero.
  • The degree (highest power) of each variable must be 1 — that is why it is called 'linear'.
2

Solutions of a Linear Equation in Two Variables

  • A solution of a linear equation in two variables is an ordered pair (x, y) that satisfies the equation.
  • An ordered pair is written as (x, y) — the x-value always comes first.
  • A linear equation in two variables has INFINITELY MANY solutions.
3

Word Problems – Forming Linear Equations

  • Real-world situations can be expressed as linear equations in two variables.
  • Identify the two unknown quantities and assign variables to them (usually x and y).
  • Translate the relationship given in the problem into a mathematical equation.
4

Graph of a Linear Equation in Two Variables

  • The graph of a linear equation in two variables is always a STRAIGHT LINE.
  • Every point (x, y) on the line is a solution of the equation, and every solution is a point on the line.
  • To draw the graph: find at least two solutions (ordered pairs), plot them on the Cartesian plane, and join them with a straight line.

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Full Notes

Key Concepts

A linear equation in two variablesMany equations that look different atA solution of a linear equationTo find solutions systematicallyUnlike linear equations in one variable

Frequently Asked Questions

What are the important topics in Linear Equations in Two Variables for Gujarat Board Class 9 Mathematics?
Key topics in Linear Equations in Two Variables include Decision tree to identify linear equations in two variables, Step-by-step process for converting equations to standard form, Process to verify if an ordered pair is a solution. These are the concepts Gujarat Board Class 9 examiners draw on most — study them first, then practise related questions.
How to score full marks in Linear Equations in Two Variables — Gujarat Board Class 9 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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