We are looking for the length and width of the rectangular pool. So let $L$ represent the length and $W$ represent the width. The perimeter of the rectangular pool is $68$ yards. Using the perimeter formula, this gives us one equation for our system: $$68=2L+2W$$ The length of the pool is two yards longer than three times its width. This translates into the following equation: $$L=3W+2$$ Hence, our system is as follows: $$\begin{cases} 68=2L+2W \\ L=3W+2 \end{cases}$$ This system can be easily solved by substitution since the second equation already has $L$ isolated. Thus, the first step in solving this system is to substitute the expression $3W+2$ in place of $L$ in the first equation. Then, we solve for $W\text{.}$ This will give us: $$\begin{gathered} 68=2(\substitute{3W+2})+2W\\ 68=6W+4+2W\\ 68=8W+4\\ 64=8W\\ W=8 \end{gathered}$$ Therefore, the width of the pool is $8$ yards. To find the length of the pool, we can substitute $8$ in place of $W$ in the second equation: $$\begin{gathered} L=3(\substitute{8})+2\\ L=24+2\\ L=26 \end{gathered}$$ Thus, length of the pool is $26$ yards. The check is left to the reader.