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Revision Notes
Pair of Linear Equations in Two Variables — Revision Notes
Punjab Board · Class 10 · Mathematics
Pair of Linear Equations in Two Variables revision notes for Punjab Board Class 10 Mathematics: 4 topics in quick points.
45 questions30 flashcards4 formulas & key relations5 concepts
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Key Topics to Revise
1
General Form and Basic Concepts
- The general form of a linear equation in two variables is: a₁x + b₁y + c₁ = 0, where a₁, b₁, and c₁ are real numbers and a₁ ≠ 0, b₁ ≠ 0.
- A pair of linear equations in two variables is also called a system of simultaneous linear equations.
- The solution of a pair of linear equations is an ordered pair (x, y) that satisfies both equations at the same time.
2
Ratio Conditions and Nature of Solutions
- By comparing the ratios a₁/a₂, b₁/b₂, and c₁/c₂, we can determine the nature of the solution WITHOUT actually solving the equations.
- CONDITION 1 — Unique Solution (Intersecting Lines, Consistent): a₁/a₂ ≠ b₁/b₂
- CONDITION 2 — Infinitely Many Solutions (Coincident Lines, Consistent/Dependent): a₁/a₂ = b₁/b₂ = c₁/c₂
3
Graphical Method of Solving
- In the graphical method, we draw the graphs of both equations on the same coordinate plane.
- Find at least TWO solutions (x, y) for EACH equation to draw the line accurately.
- The point where the two lines intersect gives the solution of the pair of equations.
4
Substitution Method
- In the substitution method, we express one variable in terms of the other from one equation, and substitute it into the second equation.
- This converts the system of two equations in two variables into ONE equation in ONE variable, which is easy to solve.
- After finding one variable's value, substitute it back to find the other variable.
Get complete notes with diagrams and examples
Full NotesKey Concepts
An equation of the form axTwo linear equations considered togetherFor equations a₁x + b₁y +Plot both equations as straight linesStep 1
Frequently Asked Questions
What are the important topics in Pair of Linear Equations in Two Variables for Punjab Board Class 10 Mathematics?
Key topics in Pair of Linear Equations in Two Variables include General Form and Basic Concepts, Ratio Conditions and Nature of Solutions, Graphical Method of Solving, Substitution Method. Study these first, then practise questions on each for the Punjab Board Class 10 board exam.
How should I revise Pair of Linear Equations in Two Variables for the Punjab Board Class 10 board exam?
Learn the core ideas first, then work through the 45 practice questions on Pair of Linear Equations in Two Variables. Revise definitions regularly and use flashcards for quick recall before the exam.
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