SOLUTION: solve the system x+y+z=6 3x+4y-7z=1 2x-y+3z=5

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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