Question 90768


         Solve the system by substitution.
x + y = 12
y = 2x 

Solve the system by addition.
5x – 3y = 13
4x – 3y = 11


   1) x+y = 12.....(1)

       y = 2x.......(2) 

        substitute  for y in (1)

          x+2x = 12 
            3x = 12   or x = 12/3 = 4 

          y = 2*4 = 8

   The    required solution is x = 4  and y = 8


  2)5x-3y =13.....(1)

    4x-3y = 11.....(2)

       multiply (2) by -1 and add to (1)

            5x-3y = 13
           -4x+3y = -11
      we get x = 2  because -3y   &  3y gets cancelled

           substitute for x in (1)

             5*2-3y = 13

             10-13 = 3y
                 3y = -3  or  y = -1

        The solution is x = 2   and y = -1