Expert: Paul Klarreich - 2/2/2009

Question
QUESTION: hey there Paul,
I'm a student in year 12 in australia and have a question about multi equation simultaneous.
Well, for example:
x+2y-z=2
2x-y+2z=5
x+y-z=1
Find x, y, z.
I keep trying different methods and nothing seems to be working. Please help!
Thanks, Ray

ANSWER: Questioner:   Ray
Category:  Advanced Math
Private:  No
 
Subject:  3 equation simutaneous equations?
Question:  hey there Paul,

I'm a student in year 12 in australia and have a question about multi equation simultaneous.

>> In Australia, your summer is winter and your night is day and your today is tomorrow (at least when I watch your Australian Open tennis, now on 24/7 here), so year 12 must be the first one, right, mate?
...........

Well, for example:
x+2y-z=2
2x-y+2z=5
x+y-z=1
Find x, y, z.
I keep trying different methods and nothing seems to be working. Please help!
Thanks, Ray
...................................
Hi, Ray,

Sorry about that.  I'll try to focus on the math.

In

x + 2y -  z = 2    A
2x  - y + 2z = 5    B
x  + y -  z = 1    C

You should have told me which methods you tried, because there are several.  But the most obvious method is to eliminate one of the variables:

How about z?

x + 2y -  z = 2    A
-x  - y +  z = 1   - C
--------------------------
     y      = 1  A-C

Hmmmmmm...  Too easy?

But now just put y = 1 back into the first and second equations:

x + 2  -  z = 2    A
2x - 1 +  2z = 5    B


x      -  z = 0    A
2x     +  2z = 6    B

x     -  z = 0    A
x     +  z = 3    B   <<< divide out the 2
-----------------------
2x          = 3         << add.
x = 3/2.  

3/2 + 2  -  z = 2    A  << put back  x = 3/2, y = 1
   3/2 - z = 0
   3/2 = z

Solution is  (3/2,1,3/2)

A smart bloke like you can handle fractions, ok, mate?

Oops.  I guess I should have said:

A smart Sheila like you can handle fractions, ok, mate?

[Is that what you use for a girl?]



---------- FOLLOW-UP ----------

QUESTION: Sorry this is not a question, it;s just that the computer wont let me click on the rate button. Yes, sheila is the correct term for a girl. Very good.

Answer
It is because I have the 'rate' option turned off currently.  I have received enough ratings from some nasty people.  [which does not include you, of course.]

Your comments are appreciated.  Feel free to send more questions.  Perhaps you will want to hear about Gauss-Jordan reduction, or Cramer's Rule.