SOLUTION: Solve the following 3 by 3 system algebraically. x+y+2z=0 1/4x-1/4y+1/8z=1 3/2x+y+1/2z=1

Algebra ->  College  -> Linear Algebra -> SOLUTION: Solve the following 3 by 3 system algebraically. x+y+2z=0 1/4x-1/4y+1/8z=1 3/2x+y+1/2z=1      Log On


   

Question 271696: Solve the following 3 by 3 system algebraically.
x+y+2z=0
1/4x-1/4y+1/8z=1
3/2x+y+1/2z=1
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
I'm not sure what "algebraically" means.
-------------
x+y+2z=0
1/4x-1/4y+1/8z=1 --> 2x-2y+z = 8
3/2x+y+1/2z=1 --> 3x+2y+z = 2
---------------
x + y+2z = 0
2x-2y +z = 8
3x+2y +z = 2
Eliminate y
------------
Add eqns 2 and 3
2x-2y +z = 8
3x+2y +z = 2
------------- Add
5x + 2z = 10 eqn A
--------------
Add 2x 1st eqn to 2nd
2x+2y+4z = 0
2x-2y +z = 8
------------Add
4x + 5z = 8 eqn B
20x +25z = 40 eqn B x 5
20x + 8z = 40 eqn A x 4
------------------------ Subtract
17z = 0
z = 0
------
x = 2
-----
y = -2