\begin{tabular}{l}\( 3 x-2 y=2 \) \\ \( 2 x-2 y=6 \) \\ Enable Zoom/Pan \\ \hline\end{tabular}

Let's take a stroll down memory lane! Systems of equations like the one you’ve got were essential to the development of algebra. Mathematicians like René Descartes and Isaac Newton contributed to these concepts, which helped lay the groundwork for calculus and modern science. Who knew solving for \(x\) and \(y\) could hold the keys to such incredible advancements? Now, when dealing with systems like this, be vigilant! A common mistake is neglecting to align the equations correctly. If you're using substitution or elimination, always double-check that your operations maintain balance. And remember: if an equation simplifies to a statement like \(0 = 0\), you have infinitely many solutions—like finding hidden treasure in the depths of math!