From point to point

Can you combine vectors to get from one point to another?

Problem



How can you get from $(10,66)$ to  $(20,12)$

using only integer multiples of the vectors

$\begin{pmatrix}2\\-3\end{pmatrix}$ and $\begin{pmatrix}3\\2\end{pmatrix}$?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.