Question 89045

   i. Explain how to apply elimination in solving a system of equations. 
ii. Explain how to apply substitution in solving a system of equations. 
iii. Demonstrate each technique in solving the system 


     
   To solve a system of linear equation  by elimination  process

   1)Bring the co-efficient of any one variable to the same .

   2)  If the signs of both variable are same  (having the same co-efficients)
         then subtract the two eq's.

   3)If the signs are different   then add the two eq'ns   so that like terms get eliminated.
      
   4)The value of one variable is calculated
  
   5)By subtituting the value of known variable   unknown variable can be 

         found.

    solution: 1. 3x + 9y = 12 

               2. 5x - 4y = 3 

             1)L.C.M  of 3,5 = 15 hence bring the co-efficient of x to 15

               multiply eq'n(1) by 5 ,  and eq'n(2) by 3. The two eq'ns 

               reduces to  15x+45y = 60
                           15x-12y = 9

              2) subtract the two  eq'ns  we get  57y = 51 , y = 51/57

              3) substituting the value of y in eq'n (1) we get
 
                    3x+9(51/57) = 12

                             3x = 12- (459/57) = 684-459/57 = 225/57

                             x = 225/57*3 = 75/57 

                   solution is x = 75/57   and y = 51/57