$\begin{gathered}
  \left\{ \begin{gathered}
  3x + y = 3\,\,\, \hfill \\
  4x + 2y = 2 \hfill \\ 
\end{gathered}  \right. \Rightarrow \underline {\left\{ \begin{gathered}
   - 6x - \cancel{{2y}} =  - 6 \hfill \\
  4x + \cancel{{2y}} = 2\,\,\,\,\,\, \hfill \\ 
\end{gathered}  \right.}  \hfill \\
  \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, - 2x =  - 4 \hfill \\
  \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x = \frac{{ - 4}}{{ - 2}} \hfill \\
  \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x = 2 \hfill \\ 
\end{gathered} $

$3 \times \left( 2 \right) + y = 3$
$6 + y = 3$
$y = 3 - 6$
$y =  - 3$