Find the ordered pair $(s, t)$ that satisfies the system \begin{align*} \dfrac{s}{2} + 5t &= 3,\\ 3t - 6s &= 9. \end{align*}

Axel follows these steps to divide 40 by 9: start with 40. 1. divide by 9 and write down the remainder. 2. write a zero after the remainder. 3. repeat steps 1 and 2 until you have a remainder of zero. examine his work, and then complete the statements below.