SOLUTION: Please help... I tried to solve this, but no result. I eliminated z in 1&2,and 2&3, but both was 7x+5y=13. How can I get the answer as an ordered triple (x,y,z)? solve the syste

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Question 1091411: Please help... I tried to solve this, but no result.
I eliminated z in 1&2,and 2&3, but both was 7x+5y=13. How can I get the answer as an ordered triple (x,y,z)?
solve the system for x,y,z
2x+3y-z=4 ....1)
3x-y+2z=5.....2)
x-4y+3z=1.....3)
Thank you.
Found 2 solutions by htmentor, ikleyn:
Answer by htmentor(1343)   (Show Source): You can put this solution on YOUR website!
What you have found is that there is not a unique solution to this system of equations.
We have 3 unknowns but only 2 independent equations.
In this case, there are infinitely many solutions.
Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
.
Notice that if you add the equations (1) and (3) (both sides), you will get exactly the equation (2).


It means that the three equations (1),(2) and (3) are dependent.


On the physical level, it means that the equations (1),(2) and (3) carry the same information, as the only two equations (1) and (3).


So, you actually have two equations for three unknowns.

Therefore, it is not amazing that the system has infinitely many solutions.



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