SOLUTION: . x + 3y − z = a x + y + 2z = b 2y − 3z = c solve the following systems, where a, b, and c are constants.

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Question 1122615: . x + 3y − z = a
x + y + 2z = b
2y − 3z = c
solve the following systems, where a, b,
and c are constants.
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
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. x + 3y − z = a
x + y + 2z = b
2y − 3z = c
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From first two equations, a-3y%2Bz=b-y%2B2z
-3y%2Bz%2By-2z%2Ba=b
-2y-z=b-a
2y%2Bz=a-b

Revision to simpler system:
system%282y%2Bz=a-b%2C2y-3z=c%29

2y%2Bz-2y-%28-3z%29=a-b-c
4z=a-b-c
highlight%28z=%28a-b-c%29%2F4%29


Returning to system%282y%2Bz=a-b%2C2y-3z=c%29
system%286y%2B3z=3a-3b%2C2y-3z=c%29
Add corresponding members,
8y=3a-3b%2Bc

highlight%28y=%283a-3b%2Bc%29%2F8%29


from the very first equation, x=a-3y%2Bz
substitute for y and z, simplify from that.