I am trying to solve an exercise with partial derivatives. I have no issue with the derivation part, but once you do that you are supposed to solve a system of equations to find the solution. I already did a few exercises of this kind. However, I found one with a particular system of equations that I can not figure out how to solve. Multiplying one equation by something to delete one variable and solve the other one does not seem to work. I need to know the value of $\frac{\partial x}{\partial u}$ and $\frac{\partial y}{\partial u}$.
Said system of equations is:
$ \left\{ \begin{aligned} \left(2x+y\right)\frac{\partial x}{\partial u}+x\frac{\partial y}{\partial u}=-2 \\ y\frac{\partial x}{\partial u}+\left(x-2y\right)\frac{\partial y}{\partial u}=-1 \\ \end{aligned} \right. $
The answers are supposed to be: $\frac{\partial x}{\partial u}=\frac{4y-x}{2\left(x^2-2xy-y^2\right)}$ and $\frac{\partial y}{\partial u}=\frac{y-2x}{2\left(x^2-2xy-y^2\right)}$