SOLUTION: Solve the system 2x-3y+z=13 x+2y+3z=2 3x-y+z=12

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Question 477998: Solve the system
2x-3y+z=13
x+2y+3z=2
3x-y+z=12
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

2x-3y%2Bz=13.....1
x%2B2y%2B3z=2.......2
3x-y%2Bz=12.......3
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2x-3y%2Bz=13.....1...solve for z
z=-2x%2B3y%2B13..........plug in 3
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3x-y%2B%28-2x%2B3y%2B13%29=12.......3
3x-y-2x%2B3y%2B13=12
x%2B2y=12-13
x%2B2y=-1............solve for x
x=-2y-1.
----------------------------

z=-2x%2B3y%2B13...plug in x
z=-2%28-2y-1%29%2B3y%2B13
z=4y%2B2%2B3y%2B13
z=7y%2B15....plug in 2 along with x=-2y-1
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x%2B2y%2B3z=2....2
%28-2y-1%29%2B2y%2B3%287y%2B15%29=2
-2y-1%2B2y%2B21y%2B45=2
21y%2B44=2
21y=2-44
21y=-42
y=-42%2F21

y=-2.............the solution .....plug in x=-2y-1
x=-2%28-2%29-1
x=4-1
x=3...........the solution

now find z
z=7y%2B15
z=7%28-2%29%2B15
z=-14%2B15
z=1..........the solution

so, solutions are:
x=3
y=-2 and
z=1
check:

2x-3y%2Bz=13.....1
2%283%29-3%28-2%29%2B1=13
6%2B6%2B1=13
13=13