That's A Lot Of Equations

Logic Level 3

\[ \begin{array} { c c c c c } \square & + & \square & = & \square \\ \square & + & \square & = & \square \\ \square & + & \square & = & \square \\ \square & + & \square & = & \square \\ \square & + & \square & = & \square \\ \square & + & \square & = & \square \\
\end{array} \] Is it possible to fill the above squares with all the integers from 1 to 18 (using each number only once), such that each equation holds true?

For example, if we had only 4 rows and 12 numbers from 1 to 12 available, we could do the following:
\[ \begin{array} { c c c c c } 1 &+& 6 & =& 7 \\ 2 &+& 10 & =& 12 \\ 3 &+& 8 & =& 11 \\ 4 &+& 5 & =& 9. \end{array} \]

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