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