Lesson on Simultaneous equations.

​How to solve simultaneous equations using the elimination method.

This involves adding or subtracting simultaneous equations (or multiples of equations) to eliminate one of the unknowns.This leave



  2.
  Note:A different way of saying the above concept is whether the unknowns have the same co-efficients (sign and absolute value).
  This leads to 4 cases to be looked at separately.

                                                                       SAME SIGN                        DIFFERENT SIGN
  SAME NUMBER                                              case 1                                  case 2
  DIFFERENT NUMBER                                     case 3                                  case 4

  General approach to eliminating an unknown.
  A.First decide which unknown ( x or y ) you wish to eliminate.
  B.Be sure that this unknown has the same co efficient in front of it if necessary by multiplying one or both equations.
  C.If the unknowns have the same sign,subtract the equations
  D.if the unknowns have different signs add the equations.

  Note:Elimination leaves one equation with one unknown,which can be solved to find the unknown which was eliminated ( x or y ).Either unknown can be found.
  Case 1.Elimination method with unknowns having the same sign and same co efficient.
            X + Y = 5..........1
                                             ( co efficients of X are negative and have same number.)
            X -  Y = 1..........2
   We can eliminate the X by subtracting equation 2 from equation 1.Thus, 1.           X + Y = 5
                                                                                                            2.           X -  Y = 1   (subtract equation 2 from equation 1) thus
                                                                                                            1.           X + Y = 5
                                                                                                            2.         - X -  Y = 1
                                                                                                                              2Y = 4
  Note the X term has been eliminated.One equation in one unknown is left which can be solved to find the unknown.This value can then be substituted
  into one of the original simultaneous equations using algebra to find the other unknown.

  Case 2.Elimination method with different signs and same number.
          X + Y = 5...............1
          X -  Y = 1...............2
                                                                                                           1.           X + Y = 5
                                                                                                           2.         +X -  Y = 1
                                                                                                                       2X       = 6
   We solve for the unknown (X) using substitution method.


SOLVE THIS EQUATION:

2 L +  2 W  = 124

L = 5W - 10
SOLVE:

L = 5W - 10 ; 2L + 2W = 124

2(5W - 10) + 2W = 124   .......................Clear parenthesis

12w - 20 =  124   .................................Collect the terms

12w - 20 =  124...................................Simplify by adding like terms (20) to both sides

w  =  12    ..........................................Isolate by dividing





​For the rule y =  - 2x + 1 calculate the y values that complete the table.