Question 1
Find all real numbers $x,y$ such that
$$\begin{cases}\sqrt{3x}\left(1+\dfrac1{x+y}\right)=2,\\[3pt]\sqrt{7y}\left(1-\dfrac1{x+y}\right)=4\sqrt2.\end{cases}$$
$$\begin{cases}\sqrt{3x}\left(1+\dfrac1{x+y}\right)=2,\\[3pt]\sqrt{7y}\left(1-\dfrac1{x+y}\right)=4\sqrt2.\end{cases}$$