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Pair of Linear Equations in Two Variables — Revision Notes

Madhya Pradesh Board · Class 10 · Mathematics

Pair of Linear Equations in Two Variables revision notes for Madhya Pradesh Board Class 10 Mathematics: 4 topics in quick points.

128 questions56 flashcards4 formulas & key relations5 concepts

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An illustration showing a real-world scenario (Akhila at a fair with a Giant Wheel and Hoopla game) that can be modeled by a pair of linear equations in two variables.
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Key Topics to Revise

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1. Basic Ideas and Types of Solutions

  • A pair of linear equations in two variables can be written in general form as a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0.
  • The lines may intersect in a single point, giving a unique solution and a consistent pair of equations.
  • The lines may be parallel, giving no solution and an inconsistent pair of equations.
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2. Graphical Method and Its Interpretation

  • A graphical solution is found by drawing both lines and identifying their point of intersection.
  • If the lines intersect, the solution is the coordinates of the common point.
  • If the lines coincide, every point on the line is a solution.
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3. Substitution Method

  • The substitution method is called so because one variable is substituted by expressing it in terms of the other.
  • First, write one variable in terms of the other from one equation.
  • Then substitute that expression into the second equation.
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4. Elimination Method

  • The elimination method is called so because one variable is eliminated first to get a linear equation in one variable.
  • First multiply the equations by suitable non-zero constants so that the coefficients of one variable become equal.
  • Then add or subtract the equations to eliminate that variable.

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Full Notes

Key Concepts

A pair of linear equationsA pair is consistent if itIntersecting lines give one solutionIf a1/a2 ≠ b1/b2Two straight lines are drawn from

Frequently Asked Questions

What are the important topics in Pair of Linear Equations in Two Variables for Madhya Pradesh Board Class 10 Mathematics?
Key topics in Pair of Linear Equations in Two Variables include Basic Ideas and Types of Solutions, Graphical Method and Its Interpretation, Substitution Method, Elimination Method. Study these first, then practise questions on each for the Madhya Pradesh Board Class 10 board exam.
How should I revise Pair of Linear Equations in Two Variables for the Madhya Pradesh Board Class 10 board exam?
Learn the core ideas first, then work through the 128 practice questions on Pair of Linear Equations in Two Variables. Revise 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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All Madhya Pradesh Board Class 10 Mathematics Revision Notes

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