Expert: Paul Klarreich - 2/22/2007

Question
answer as an ordered triple

x+y+z=3
2x+-y=2
4z=2x+2y

Answer
Questioner:   Sam
Category:  Advanced Math
Question:  answer as an ordered triple

x+y+z=3
2x+-y=2    <<< Did you mean to write  =-?
4z=2x+2y
..............................
Hi, Sam,

This is just simultaneous equations, which you solve by whatever method goes fastest.
Your last equation can be rewritten:
4z = 2x + 2y
2z = x + y
- x - y + 2z = 0

and you have this system:

 x +  y  +  z  =  3 (I)
2x -  y        =  2 (II)
- x -  y  + 2z  =  0 (III)

How about eliminating y by adding the first equation to each of the others:

3x   +  z = 5   (I + II = IV)
      3z = 3   (I + III = V)

How about that?  The last equation gives  z = 1.  Put that back into IV:

3x + 1 = 5
x = 4/3  [Yuk.  But we have seen fractions before, right?]
Now back into equation I:

4/3 + y + 1 = 3
4/3 + y   = 2
y = 2/3

So, as an ordered triple, your solution is (4/3, 2/3, 1)