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Revision Notes
Linear Equations in Two Variables — Revision Notes
Punjab Board · Class 9 · Mathematics
Linear Equations in Two Variables revision notes for Punjab Board Class 9 Mathematics: 3 topics in quick points.
45 questions30 flashcards3 formulas & key relations5 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 NotesKey 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 What is a Linear Equation in Two Variables?, Solutions of a Linear Equation in Two Variables, Graph of a Linear Equation in Two Variables. Study these first, then practise questions on each for Class 9 exams.
How should I revise Linear Equations in Two Variables for Class 9 exams?
Learn the core ideas first, then work through the 45 practice questions on Linear Equations in Two Variables. Revise definitions regularly and use flashcards for quick recall before the exam.
Sources & Official References
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