\( \left. \begin{array} { l } { 12 x + 4 y = 20 \ldots \ldots . . . ( 6 ) } \\ { 7 x - 3 y = 19 \ldots \ldots . ( 6 ) } \end{array} \right. \)

Did you know that the context of solving systems of equations dates back to ancient civilizations like the Babylonians? They used similar methods to solve problems related to trade and land division, showcasing the early application of algebraic concepts in practical scenarios. Imagine how they must have felt discovering these techniques to make sense of their numerical puzzles! In today's world, systems of equations can be applied in various fields such as economics, engineering, and data analysis. For instance, businesses often need to determine the optimal combination of products to maximize profit based on constraints like budget or resource availability. By setting up equations, they can accurately model and solve these real-life problems, making algebra a critical tool for decision-making!