SOLUTION: I'm not sure if I'm in the right place but here it goes. I can't seem to figure out this problem. You have to solve for 3 variable and you're given 3 equations, but I can't solve i

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Question 670879: I'm not sure if I'm in the right place but here it goes. I can't seem to figure out this problem. You have to solve for 3 variable and you're given 3 equations, but I can't solve it. The problem is:
x + y + z = 0
2x + 3y + 2z = -1
x - y + z = 2

Found 3 solutions by Alan3354, lynnlo, vleith:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website!
x + y + z = 0
2x + 3y + 2z = -1
x - y + z = 2
---------------
Add eqn 1 and 3
2x + 2z = 2 --> x + z = 1
-------------
2x + 3y + 2z = -1
x - y + z = 2 times 3 --> 3x - 3y + 3z = 6
----
3x - 3y + 3z = 6
2x + 3y + 2z = -1 (eqn 2)
---------------------- Add
5x + 5z = 5
--> x + z = 1
----
Same as the 1st result --> dependent, no unique solution.

Answer by lynnlo(4176)   (Show Source):
You can put this solution on YOUR website!
x=-y-z,y=-1

Answer by vleith(2983)   (Show Source):
You can put this solution on YOUR website!
3 variables and 3 unknowns says you might have a solution. It doesn't mean there MUST be one.
take the first and third equations and add them

---------------------
remember this
Now look at the second equation

sub in from above

Plug y into the three original equtions, shows all three equations to be the same equation. So 1 equation with 2 unknowns, and you can;t solve that.
Another wya to look at this, solve the first and third equations for y

the only way that works is y=0.
If you set y = 0 in the first anf thrid equations, the and clearly that can't be,
So there is no solution to this one.