7. \( \begin{array}{r}x-y=-2 \\ -x+y=2\end{array} \)

Let's revisit the history of simultaneous equations! The method of solving such equations can be traced back to ancient civilizations, notably the Babylonians around 2000 BC. They used geometric interpretations that eventually evolved into the algebra we know today. Fast forward to the 16th century, and mathematicians like Gerolamo Cardano were formalizing these methods, paving the way for the systematic techniques we often employ now. Now, onto solving your equations! A simple way to approach this system is to add both equations together. So, \(x - y + (-x + y) = -2 + 2\) simplifies to \(0 = 0\), indicating that both equations represent the same line. This means there are infinitely many solutions, as any point on the line defined by either equation will satisfy both! Try it out by substituting some values for \(y\) to see the corresponding \(x\) values!