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Linear Equations in Two Variables

Punjab Board · Class 9 · Mathematics

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

45 questions30 flashcards5 concepts

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Key Topics to Revise

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1. What is a Linear Equation in Two Variables?

  • A linear equation in two variables has the standard form: ax + by + c = 0, where a, b, c are real numbers and a and b are NOT both zero simultaneously.
  • The variables are most commonly denoted by x and y, but other letters like s, t, p, q, u, v can also be used.
  • Examples: 2x + 3y = 9, x − 4 = √3y, 4 = 5x − 3y, πu + 5v = 9
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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 when substituted.
  • The order matters: (3, 2) and (2, 3) are DIFFERENT ordered pairs. Always write (x-value, y-value).
  • A linear equation in two variables has INFINITELY MANY solutions — you can never list all of them.
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3. Graph of a Linear Equation in Two Variables

  • The graph of a linear equation in two variables is always a STRAIGHT LINE.
  • To draw the graph: Find at least 2 solutions (ordered pairs), plot them as points on the Cartesian plane, and join them with a straight line extending in both directions.
  • Every point ON the line is a solution of the equation. Every point NOT on the line is NOT a solution.

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Full Notes

Key Concepts

A linear equation in two variablesAny linear equation in two variablesA solution to a linear equationUnlike linear equations in one variableThere are simple techniques to find

Frequently Asked Questions

What are the important topics in Linear Equations in Two Variables for Punjab Board Class 9 Mathematics?
Key topics in Linear Equations in Two Variables include Problem-Solving Strategy for Linear Equations in Two Variables, Mind map showing the definition, structure, and characteristics of linear equations in two variables, Flowchart showing the step-by-step process of converting equations to standard form. These are the concepts Punjab 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 — Punjab 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.

More resources for Linear Equations in Two Variables

All 5 chapters — Punjab Board Class 9 Mathematics Revision Notes

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