b) \( \left\{\begin{array}{l}3 x+4 y=1 \\ 3 x-y=11\end{array}\right. \)

Let's get a little historical here: the method of solving systems of linear equations dates back to ancient civilizations! If you think about it, the Babylonians were already solving similar problems around 2000 BC, using a form of algorithmic reasoning. This mathematical technique has evolved over the centuries, influencing modern algebra and serving as the foundation for complex problem-solving in today's mathematics. Now, onto some real-world applications! Systems of equations are often used in economics to find equilibrium prices, in engineering to determine forces in structures, and even in computing algorithms for optimization problems. So next time you're using a calculator or even debating price tags at the store, remember that you're tapping into this powerful mathematical tool that has real-world significance!