\documentclass{jarticle}
\usepackage{amsmath,cases}

\begin{document}

$$
\left\{
\begin{array}{r@{\,}c@{\,}r@{\,}c@{\,}r@{\;\leq\;}r}
 x_1&+& x_2& &      &120,\\
2x_1&+&      & &3x_3&150,\\
      & &4x_2&+&5x_3&340
\end{array}%
\right.
$$

$$
\left\{
\begin{array}{r@{\,}r@{\,}r@{\,}r}
 x_1& + \hphantom{4}x_2&\phantom{+5x_3}&\leq 120,\\
2x_1& + \hphantom{4x_2}&        +3x_3 &\leq 150,\\
    & \hphantom{+}4x_2 & + 5x_3       &\leq 340.
\end{array}
\right.
$$

\begin{equation}
\left\{
\begin{array}{r@{\,}r@{\,}r@{\,}r}
 x_1& + \hphantom{4}x_2&\phantom{+5x_3}&\leq 120,\\
2x_1& + \hphantom{4x_2}&        +3x_3 &\leq 150,\\
    & \hphantom{+}4x_2 & + 5x_3       &\leq 340.
\end{array}
\right.
\end{equation}

\begin{subnumcases}
{}
\hphantom{2} x_1 + \hphantom{4}x_2\phantom{+5x_3}\ \leq & \hspace{-18pt}120,\\
            2x_1 + \hphantom{4x_2}        +3x_3    \leq & \hspace{-18pt}150,\\
   \hphantom{2x_1+}\ 4x_2  + 5x_3                  \leq & \hspace{-18pt}340.
\end{subnumcases}


$$
\begin{cases}
 x_1 +  x_2        \leq 120,\\
2x_1 +       3x_3 \leq 150,\\
       4x_2 + 5x_3 \leq 340.
\end{cases}
$$

$$
\left\{
\begin{array}{rrrr}
 x_1& +\  \hphantom{4}x_2&\ \phantom{+5x_3}&\leq 120,\\
2x_1& +\  \hphantom{4x_2}&+\          3x_3 &\leq 150,\\
    &             4x_2   &+\  5x_3         &\leq 340.
\end{array}
\right.
$$

$$
\left\{
\begin{array}{llll}
 x_1& + \hphantom{4}x_2&\phantom{+5x_3}&\leq 120,\\
2x_1& + \hphantom{4x_2}&        +3x_3 &\leq 150,\\
    & \hphantom{+}4x_2 & + 5x_3       &\leq 340.
\end{array}
\right.
$$

\begin{align*}
\hphantom{2}x_1 + \hphantom{4}x_2\phantom{+5x_3}&\leq 120,\\
2x_1 + \hphantom{4x_2}         +3x_3 &\leq 150,\\
                        4x_2  + 5x_3 &\leq 340.
\end{align*}

\end{document}
