what are some typical systems of equations generating from practical problems?Some examples or research articles...

Systems of equations come up all the time. In programming models, we seek to optimize $cx$ with respect to a constraint $Ax\le b$, where $A$ is a matrix, $c$ and $b$ are vectors, and $x$ is the vector we are changing to maximize the system. The system of equations is $Ax\le b$.
Linear programming is used all the time in economics for market optimization, insurance purchase optimizations, contractual optimizations, game theory, etc.
Linear programming and integer programming also come up in graph theory with network flows (which are practical in terms of fluid or electrical flows), shortest path algorithms, knapsack problems, and such.