SOLUTION: Solve the system of equations: x+y+z=1 3x-2y-z=5 x+3y+2z=3 (Enter your answer as an ordered triple.) Thanks.

Algebra ->  Linear-equations -> SOLUTION: Solve the system of equations: x+y+z=1 3x-2y-z=5 x+3y+2z=3 (Enter your answer as an ordered triple.) Thanks.      Log On


   

Question 985100: Solve the system of equations:
x+y+z=1
3x-2y-z=5
x+3y+2z=3
(Enter your answer as an ordered triple.)
Thanks.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

same as Question 985109
x%2By%2Bz=1.......eq.1
3x-2y-z=5.......eq.2
x%2B3y%2B2z=3 .......eq.3
------------------------------------------------
x%2By%2Bz=1.......eq.1
3x-2y-z=5.......eq.2
------------------------------------------add
x%2By%2Bcross%28z%29%2B3x-2y-cross%28z%29=1%2B5
x%2By%2B3x-2y=6
4x-y=6...............solve for y
y=4x-6.........eq.1a

x%2By%2Bz=1.......eq.1....multiply by 2
x%2B3y%2B2z=3 .......eq.3
------------------------------------
2x%2B2y%2B2z=2.......eq.1
x%2B3y%2B2z=3 .......eq.3
---------------------------------------- subtract
2x%2B2y%2Bcross%282z%29-x-3y-cross%282z%29=2-3.
2x%2B2y-x-3y=-1
x-y=-1........solve for y
y=x%2B1..............eq.2a
from eq.1a and eq.2a we have
4x-6=x%2B1......solve for x
4x-x=6%2B1
3x=7
x=7%2F3
go to y=x%2B1..............eq.2a, substitute 7%2F3 for x
y=7%2F3%2B1
y=7%2F3%2B3%2F3
y=10%2F3
go to x%2By%2Bz=1.......eq.1, substitute 7%2F3 for x and substitute 10%2F3 for y
7%2F3%2B10%2F3%2Bz=1
17%2F3%2Bz=1
z=3%2F3-17%2F3
z=-14%2F3
your answer is:(7%2F3,10%2F3,-14%2F3)