X+y=9 3x-y=9

Question

 

Subsitution or Elimination 

Answer 1

Elimination (note that equations have +y and -y already):

   x  + y  =  9

  3x  - y  =  9

------------------- [ elimination; add equations[

  4x        = 18

      x = 4.5          [divide both sides by 4]

 

   x +  y = 9

   x        = 4.5

 ----------------   [elimination; subtract equations]

          y = 4.5

 

Substitution  (solve for one variable, then use that to replace the variable in the other equation):

    x + y = 9

         y = 9-x

 

   3x - y = 9

   3x - (9-x) = 9

    3x - 9 + x = 9

     4x = 18

      x = 4.5

 

    x + y = 9

   4.5 + y = 9

      y = 4.5

 

Check (important):

  Is   4.5 + 4.5 = 9   ?

             9 = 9   ?yes

  Is  3(4.5)  - 4.5 = 9   ?

         13.5 - 4.5 = 9   ?

             9 = 9   ?yes

Answer 2

Substitution: First equation => x= 9 -y; plug in second equation => 3(9-y) - y = 9, which leads to 27 - 3y -y = 9;

so 27 -4y = 9 leads to -4y = -18 which leads to y = 4.5. Plug this in first equation and we get x = 9 - 4.5 = 4.5.