2) \( \begin{array}{l}2 x+5 y=1 \\ x-17=3 y\end{array} \)

To solve this system of equations, you can use the substitution or elimination method. If we rearrange the second equation to isolate \(y\), it becomes \(y = \frac{x - 17}{3}\). Substitute this expression for \(y\) into the first equation \(2x + 5y = 1\) to find \(x\). After plug-and-chug, you'll find \(x = 8\), and substituting \(x\) back into the equation for \(y\) gives \(y = -3\). Thus, the solution to the system is \( (8, -3) \). Now, to check your work, you can plug \(x\) and \(y\) back into both original equations. If each equation holds true, congratulations! You've successfully found the solution. If you make an error, don't fret—double-check your arithmetic, as mistakes often lurk in the details!