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

Let's add some historical context. The study of linear equations like those in your question dates back to ancient civilizations, including the Babylonians, who had methods for solving these equations over 4,000 years ago! They used geometric approaches and developed algorithms that laid the groundwork for algebra as we know it today. Now, onto how these equations can be applied in real life! Linear equations are widely used in various fields such as economics, engineering, and even in planning budgets! For example, businesses use linear models to predict sales based on varying factors or to minimize costs while maximizing profits. Solving these equations can provide valuable insights for making informed decisions.