Math help please.

[zindan]

Equation: 
−2x + 3y + 3z = −9
3x − 4y + z = 5
−5x + 7y + 2z = −14

MY solution:
x=-21-15t
y=-17-11t
z=t


The correct answer is however 
x = -21 +15t
y = -17 + 11t
z =-t

My only misstake was putting z = t instead of z = -t which I don't even understand how the negative 1 comes in?  I mean I thought parameter solutions could be anything so why -t? I don't get it? 
 

[zindan]

BUMP

[Evrion]

yes, you can choose whatever you want for the parameter.

 

I suspect the book or teacher or whatever has some principle about "choose the parameter that gives no fractions, and has the X coefficient as a positive number".

[Dash Lambda]

Did your teacher really mark you down for that? 'Cause you're right, the difference is just in representation.