SOLUTION: I am trying to solve a system of equations with three variables. 6x-y+2z=-14 x+2y-z=-2 2x+2y-3z=-11 I am new to algebra and have never done an equation with three variables.

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: I am trying to solve a system of equations with three variables. 6x-y+2z=-14 x+2y-z=-2 2x+2y-3z=-11 I am new to algebra and have never done an equation with three variables.       Log On


   

Question 818979: I am trying to solve a system of equations with three variables.
6x-y+2z=-14
x+2y-z=-2
2x+2y-3z=-11
I am new to algebra and have never done an equation with three variables. I know I am supposed to take two of the equations so that I can eliminate one variable, such as x, but I am unsure on which two I should choose. If anyone can help me solve this, and show me each step in doing so it would be appreciated. Thanks
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

I.    6x-y+2z=-14

II.    x+2y-z=-2

III.  2x+2y-3z=-11 



I.    12x-2y+4z=-28  |Multiplying EQ I   by 2  & adding I an II to eliminate y

II.    x+2y-z=-2

 A     13x+%2B+3z+=+-30

II.  -x-2y+z=2    |Multiplying EQ II  by -1 & adding II an III to eliminate y

III. 2x+2y-3z=-11 

 B     x+-+2z+=+-9



      13x+%2B+3z+=+-30  

      -13x+%2B26z+=+117  |Multiplying EQ B  by -13

              29z = 87

                z = 3   and x = -3  and y = 2

 2x+2y-3z=-11 

 -6 + 4 - 9 = -11