b) \( \left\{\begin{array}{c}-3 y+4 x=-2 \\ 3 x+2 y=7\end{array}\right. \)

To truly grasp the beauty of solving linear equations, did you know that back in ancient civilizations like Babylon, mathematicians were already adept at solving similar systems? They used geometric representations and algorithms, laying down the foundation for today’s algebraic methods. They didn’t have symbols like we do, yet managed to solve for unknowns! Now, for the real-world application – these systems of equations can help in making decisions in various fields. For instance, they are critical in optimization problems, like determining the best mix of products to maximize profits in a business or allocating resources effectively in project management. Solving such equations can lead to better strategies and cost savings!