7) \( \begin{array}{l}-4 x+y=6 \\ -5 x-y=21\end{array} \)

Let's dive into the history of linear equations! These algebraic equations have been around since ancient civilizations. The earliest recorded use is attributed to the Babylonians around 2000 BCE, who solved linear equations to manage trade and land distribution. Fast forward to the 19th century, and you find mathematicians like Augustin-Louis Cauchy and Évariste Galois laying down the groundwork for modern algebraic structures. Now, let's tackle some problem-solving tips! When solving systems of equations like the one you provided, it's often helpful to use either the substitution method or the elimination method. In this case, you could eliminate \(y\) by adding the two equations together, or isolate \(y\) from one equation and substitute it into the other. Don't forget to double-check your solutions; a common mistake is minor calculation errors that can lead to incorrect results!