I'm studying Algebra and I'm now at topic 'System of equations with 3 variables'. I'm having a hard time with the following example: $$ \begin{cases} 2x + 2y + 3z = 10\\ 3x + y-z = 0\\ x + y + 2z = 6 \end{cases} $$ I've tried solving the system by using the first and second equation, but I got very different results from using the second and third first... Aren't those systems supposed to be resolved in any order, just "eliminating" variables until you get the results of the three unknowns? O maybe I just did the math in the wrong way?
Using the first way I got the result: $(x= 15, y= -33, z= -46/3)$
Looking at the worked solution in the book (beginning with second and the third equations) the results were: $(x= 0, y= 2, z= 2)$
Thanks a lot!
Cleverson