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Algebraic Manipulation Techniques for Solving Equations

Learn to solve linear equations, expand brackets, factorise linear and quadratic expressions with step-by-step solutions. Enhance your algebra skills effectively.

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Algebraic Manipulation Techniques for Solving Equations

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  1. Unit 23Algebraic Manipulation

  2. Unit 23Algebraic Manipulation 23.1 Simultaneous Linear Equations

  3. Problem Solve the pair of simultaneous equations Solution In order to be able to eliminate x, we multiply the first equation by 4 and the second by 3, to give So if y = -2 we substitute back to find x, y ? ? ? ? ? Then add the equations ? ? ? ? ? ? Hence ? ?

  4. Unit 23Algebraic Manipulation 23.2 Expanding Brackets

  5. Expand Solution (a) (b) (d) (c) (a) ? ? ? (d) (c) (b) ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?

  6. Unit 21Formula 23.3 Linear Factorisation

  7. Factorise (a) (b) Solution (a) This is the reverse of the process of expanding. As 2 is a common factor of both terms, (b) The common factor of and is ? ? ? ? ? ? ? ? ?

  8. Unit 23Algebraic Manipulation 23.4 Quadratic Factors 1

  9. Factorise Solution This will be in the form of So If the possible values are ? ? ? Which of these values satisfies ? ? ? ? ? ? ? ? ? ? ?

  10. Unit 23Algebraic Manipulation 23.5 Quadratic Factors 2

  11. Factorise Solution This must be in the form So and These are the possibilities if ? ? ? Hence and ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?

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