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Simultaneous (Linear) Equations — Revision Notes

ICSE · Class 9 · Mathematics

Simultaneous (Linear) Equations revision notes for ICSE Class 9 Mathematics: 4 topics in quick points. Part of the ICSE Class 9 Mathematics syllabus.

25 questions24 flashcards9 formulas & key relations5 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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Key Topics to Revise

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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.

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Full Notes

Key Concepts

An equation of the form ax+by+c=0Two linear equations that containSolving two simultaneous linear equations meansOne variable is first writtenThe equations are multiplied by suitable

Frequently Asked Questions

What are the important topics in Simultaneous (Linear) Equations for ICSE Class 9 Mathematics?
Key topics in Simultaneous (Linear) Equations include Core Ideas and Definitions, Method of Elimination by Substitution, Method of Elimination by Equating Coefficients, Method of Cross-Multiplication. Study these first, then practise questions on each for Class 9 exams.
How should I revise Simultaneous (Linear) Equations for Class 9 exams?
Learn the core ideas first, then work through the 25 practice questions on Simultaneous (Linear) Equations. 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 ICSE Class 9 Mathematics Revision Notes

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