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Simultaneous (Linear) Equations

ICSE · Class 9 · Mathematics

Complete topic list for Simultaneous (Linear) Equations in ICSE Class 9 Mathematics. Key concepts, sub-topics, and what to focus on for board exams.

25 questions24 flashcards5 concepts

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A diagram illustrating two linear equations with two variables and their common solution point, emphasizing that they are 'simultaneous' equations.
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4 Topics · ICSE Class 9 Mathematics

Topics in Simultaneous (Linear) Equations

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1. Core Ideas and Definitions

  • A linear equation in two variables has degree 1 in each variable.
  • Simultaneous linear equations contain the same two variables and are considered together.
  • Solving two simultaneous linear equations means finding the values of the variables used in the given equations.
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2. Method of Elimination by Substitution

  • First find one variable in terms of the other from any one equation.
  • Substitute that expression into the other equation.
  • Solve the single-variable equation, then substitute back to find the second variable.
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3. Method of Elimination by Equating Coefficients

  • Multiply one or both equations so that the coefficients of x or y become numerically equal.
  • Add or subtract the equations so one variable is eliminated.
  • Solve the resulting equation and substitute back to find the other variable.
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4. Method of Cross-Multiplication

  • First write both equations in the form a1x+b1y+c1=0 and a2x+b2y+c2=0.
  • Then use the cross-multiplication formulas for x and y.
  • The arrow pattern matters: downward-arrow product is written first, then the upward-arrow product is subtracted.

Key Concepts

Central concept: Finding the values of two unknowns from two linear equations in the same two variables

Linear equation in two variablesSimultaneous linear equationsSolution of simultaneous equationsMethod of elimination by substitutionMethod of elimination by equating coefficientsMethod of cross-multiplicationEquations reducible to linear equationsWord problems based on simultaneous equations

Frequently Asked Questions

What are the important topics in Simultaneous (Linear) Equations for ICSE Class 9 Mathematics?
Simultaneous (Linear) Equations covers several key topics that are frequently asked in ICSE Class 9 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
How to score full marks in Simultaneous (Linear) Equations — ICSE Class 9 Mathematics?
Understand the core concepts first, then work through the 25 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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