Solving Simultaneous Equation Through Substitution Method

The substitution method is one of the ways through which one can solve simultaneous equations with two variables. The best way to explain it is through a worked example.


Solve the simultaneous equations using substitution method, x+2y= 3, 2x-4y= 8.

Step 1: Name the equations




                                          x+2y = 3..................(1.)



                                        2x-4y = 8..................(2.)
 
Step 2: From (1.), make x the subject of the eqn since eqn (1.) is simpler than eqn (2.).


So from (1.),

                     x+2y = 3



                    x= 3-2y.


Step 3: Now substitute for x in (2.).



So from (2.),


               2x-4y = 8 but x=3-2y



          so 2x-4y = 8 becomes



        2(3-2y)-4y= 8



          6-4y-4y = 8


              6-8y = 8



                -8y = 8-6



                -8y = 2



                   y = 2/-8

                   y = -1/4.



Step 4: To find x, substitute for y in (1.).




So from (1.),



          x+2y = 3 but y= -1/4



      so x+2y = 3 becomes



         x+2(-1/4)= 3



            x-1/2 = 3



           x = 3+1/2



           x = (6+1)/2



           x = 7/2



       So x = 7/2, y = -1/4.
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