I attempted to do the following exercise with no luck. I was sure of the answer, but apparently not.. somehow...

*The given matrix is the augmented matrix for a linear system in the variables $x\_1$, $x\_2$, and $x\_3$. Solve the system. (If there is no solution, enter **NO SOLUTION**.)* 

|$1 \ \ \ \ \ \ 0 \ \ \ \ \ \ 5 \ \ \ | \ \ \ 0$|  

|$0 \ \ \ \ \ \ 1 \ -1 \ \ \ | \ \ \ 0$|  

|$0 \ \ \ \ \ \ 0 \ \ \ \ \ \ 0 \ \ \ | \ \ \ 0$| 

*What is $(x\_1, x\_2, x\_3) = $*

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Here's what I tried.  

From the first equation, I moved the $5$ to the right side then end up with $x\_1=-5$.  

For the second equation, I moved the $-1$ to the right side to obtain $x\_2=1$.  

Finally, the third equation yields $0=0$ which can be interpreted as $t$.  

My final answer was $(x\_1, x\_2, x\_3) = (-5, 1, t)$, but supposedly it's wrong. Any help is appreciated.