SOLUTION: x-y+2z=1 x+2y+z=4 2x+y-z=5 find x y and z

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Question 209789: x-y+2z=1 x+2y+z=4 2x+y-z=5 find x y and z
Answer by silencehurts(5) About Me  (Show Source):
You can put this solution on YOUR website!
x-y+2z=1 y=x+2z
x+2y+z=4 x=-2y-z+4
2x+y-z=5 z=2x+y-5
find x y z
z= 2x +y-5
z=2(-2y-z+4)+y-5
z= -4y-2z+8 +y-5
z=-3y-2z+3
z+2z=-3y+3
3z=-3y+3
-- -----
3 3
z=-y+1

y=x+2z
y=x+2(-y+1)
y=x+(-2y+2)
y=x-2y+2
y+2y=x+2
3y-2=x

2x+y-z=5
y =5+z-2x
y =5+(-y+1)-2(3y-2)
y =5+ -y+1 - (6y-4)
y =6+ -y + -6y+4
y =10 -7y
y+7y=10
8y =10

10
y = ----
8

z=-y+1=1-y
z= 1 - 10
--
8
z= 8-10
----
8
2
z= - ---
8


3y-2=x

3(10)-2=x
--
8
30 - 16
-- -- = X
8 8
14
-- = X
8
CHECKING
2x+y-z=5
2(14) 10 (-2)
-- + -- - -- = 5
8 8 8
28 + 10 + 2
------------- = 5
8
40
-- = 5
8

5=5