Question 1799: solve the system
x+y+z=6
3x+4y-7z=1
2x-y+3z=5
Answer by longjonsilver(2297)   (Show Source):
You can put this solution on YOUR website! these are just simultaneous equations...3 unknowns and 3 equations...solvable, if tedious.
You need to start with 2 equations and get rid of 1 variable...looking at the 3 equations, use 1 and 3, as they both have a y, so easy to remove these...
1 is 
3 is 
the y's have Different signs so aDD (note the DD). Similarly, Same signs, then Subtract!!
so, we get equation 4
Now repeat the process with 2 other equations, say 2 and 3
Again I will choose to get rid of the y term, but i need to increase the lower equation by a factor of 4, to get the 2 equations to match....
The y-terms have Different signs therefore we aDD, getting equation 5...
Now we use 4 and 5 to get rid of another variable...i choose to remove the z's, by making them both 20z...
equation 4 needs to be multiplied by 5: 
equation 5 needs to be multiplied by 4:
This gives us
Here the z terms have the Same sign therefore we Subtract the 2 equations, giving us  , so x=1.
We now substitute this into 4 or 5, to find z (z=2) and then these into equation 1, 2 or 3 to find y (y=3).
THEN you double check each of the original equations (1, 2 and 3) to make sure that your answers are correct.
cheers
Jon.
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