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Simultaneous equations 1

Simultaneous equations

  • Simultaneous equations have two unknowns
  • You need to find the values for the two unknowns which make both equations true

Algebraic solution

  • Number each equation
  • If necessary, multiply the equations so that the coefficients of one unknown are the same
  • Add or subtract the equations to eliminate that unknown
  • Once one unknown is found use substitution to find the other
  • Check the answer by substituting both values into the other equation

Easier eliminations

  • You can save time by choosing the right unknown to eliminate
  • Look for one of these
    • If an unknown appears on its own in one equation you only need to multiply one equation to eliminate that unknown
    • If an unknown has different signs in the two equations tou can eliminate by adding

Check it

  • Always use the equation you didn’t substitute into to check your answer

Graphical solution

  • You can solve these simultaneous equations by drawing a graph
  • The coordinates of the point of intersection give the solution to the simultaneous equation