Expert: Steve Holleran - 2/6/2008

Question
I am having a little trouble remembering what to do with problems like these.

2x – y +3z = – 14
3x +2y + z = 7
4x +3y –2z = 27  

Answer
Hi Lynette,

Okay, the first thing is to pick a variable to eliminate first.
Let's pick y, because the coefficients are simple numbers:

I.  2x - y + 3z = -14 -----mult by 2-----> 4x - 2y + 6z = -28

II. 3x + 2y + z = 7 ---------------------> 3x + 2y + z = 7

Now add:                                   7x   + 7z = -21

I.  2x - y + 3z = -14 ----mult by 3------> 6x - 3y + 9z = -42

III.4x + 3y - 2z = 27 -------------------> 4x + 3y - 2z = 27

Add again:                                 10x + 7z = - 15


Now take the two new equations you have and eliminate a second variable. Let's get rid of the z-terms:

7x + 7z = -21 -------mult by -1 ----->  -7x - 7z = 21

10x + 7z = -15 ---------------------->  10x + 7z = -15

Add:                                     3x = 6  so x = 2

Now substitute back:  

7x + 7z = -21 -------> 7(2) + 7z = -21

                      14 + 7z = -21  so 7z = -35  and z = -5

Then, using II:  3(2) + 2y + (-5) = 7

                       2y + 1 = 7   so 2y = 6 and y = 3

You can do this by picking any of the variables to start out.

Steve