11.6.4 Systems of equations in partial derivatives of the first order

Problem: Find the general solution of the system of linear partial differential equations of the first order: \[ \left\{\begin{array}{l} \frac{\partial u}{\partial x}-\frac{\partial v}{\partial y}=0 \\ \frac{\partial u}{\partial y}-\frac{\partial v}{\partial x}=0 \end{array}\right. \]