Linear System of Equations 
I've been given:
  $$
\begin{array}{rcrcrcr}
x & + &2y &+& z &=& 3\\
x &  +& y &+& 2z &=& 2\\
 & & y&-& z &=& 1
\end{array}
$$
  Let $S$ be the set of all triples that are solutions to the system above and $$T = {(x,y,z)}={(1-3t, 1+t, t)}
$$
  I need to show that $S=T$.  

So, I tried solving for the system of equations first which got me nowhere because solving the first two equations gives us the third equation. So that was a bust.
Also, I'm not sure what to do with T?

*

*First of all, do you know how to solve a linear equation by Gaussian elimination? 

*To show $T=S$, you could show $T\subset S$ and $S\subset T$. One of the direction is trivial, can you see why?

*Note that 
$$
T = \{(1-3t, 1+t, t) \, | \, t \in \mathbb{R}\}=\{u+tv\mid t\in\mathbb{R}\}
$$
where 
$u=(1,1,0)$ and $v=(-3,1,1)$. Can you see why you should be expecting that the solution space to $Ax=0$ where $A$ is the matrix of your linear equation should be of dimension $1?$  

*Do you know how to systematically solve $Ax=0$?  
