SOLUTION: How do I find X,Y,and Z? X+y-2z=15 -x+2y+z=2 2x+3y-z=9

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Question 1045709: How do I find X,Y,and Z?
X+y-2z=15
-x+2y+z=2
2x+3y-z=9
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

x%2By-2z=15..........(1)
-x%2B2y%2Bz=2..........(2)
2x%2B3y-z=9..........(3)
start with first two equations
x%2By-2z=15..........(1)
-x%2B2y%2Bz=2..........(2)
--------------------------------add
x%2By-2z-x%2B2y%2Bz=15%2B2
3y-z=17......solve for z
z=3y-17................(1a)
go to
-x%2B2y%2Bz=2..........(2)......both sides multiply by 2
2x%2B3y-z=9..........(3)
-----------------------------
-2x%2B4y%2B2z=4..........(2)
2x%2B3y-z=9..........(3)
--------------------------------------add
-2x%2B4y%2B2z%2B2x%2B3y-z=4%2B9
7y%2Bz=13......solve for z
z=13-7y................(1b)
from 1a and 1b we have
3y-17=13-7y..................solve for y
3y%2B7y=13%2B17
10y=30
y=30%2F10
y=3
now we can find z
z=13-7y................(1b)
z=13-7%2A3
z=13-21
z=-8
now, go to x%2By-2z=15..........(1), substitute y and z and solve for x
x%2B3-2%28-8%29=15
x%2B3%2B16=15
x%2B19=15
x=15-19
x=-4
so, your solutions are:
x=-4
y=3
z=-8