Simultaneous linear equations

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What this lesson covers

  • Elimination adds or subtracts equations to remove a variable.
  • Substitution puts one equation into the other.
  • Check the answer in both equations.
Key idea

Two methods

  • Elimination: match the coefficients of one variable, then add or subtract.
  • Substitution: make one variable the subject, then replace it.
Worked example

Elimination

  • 2x + y = 7 and x − y = 2.
  1. 3x = 9add the equations
  2. x = 3
  3. 3 − y = 2
  4. y = 1

Common mistakes

  • Subtracting when the signs differ.
    Opposite signs cancel by adding.
  • Stopping after finding x.
    Find both values and check them.

Your turn

  • 1. Solve 3x + 2y = 16 and x − 2y = 0.
Show answer

1. x = 4, y = 2

Summary

What to take away

  • Line up the equations and remove one variable.
  • Check in both originals.

More in AS 91269

Simultaneous linear equationsNotesA line and a curveNotesWhat the solutions meanNotesModelling with systemsNotes

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