[tex]7)\quad x^2 = 9,\quad y^2 = 25\\ \\ x = \pm 3,\quad y = \pm 5 \\ \\ x^2-y^2 = 9-25 \\ (x-y)(x+y) = -16\\ (x-y)(\pm 3\pm 5) = -16\\ \\ x-y = \dfrac{-16}{\pm 3\pm 5}\\ \\ \Rightarrow \text{Cea mai mare valoare o are cand }x = -5\text{ si }y = 3\\ \\ \Rightarrow x-y = \dfrac{-16}{-5+3} = \dfrac{-16}{-2} = \boxed{8}[/tex]
[tex]8)\quad xy+x+y = 4\\ \\ xy+x+y+1 = 5 \\ x(y+1)+(y+1) = 5 \\ (x+1)(y+1) = 5\\ \\ \Rightarrow\left|\begin{array}{lcl}\begin{cases}x+1 = -1 \\ y+1 = -5\end{cases}\\\\\begin{cases}x+1 = 1 \\ y+1 = 5\end{cases}\end{array}\\ \right. \Rightarrow \left|\begin{array}{lcl}\begin{cases}x = -2 \\ y= -6\end{cases}\\\\\begin{cases}x=0 \\ y=4\end{cases}\end{array}\\ \right.\vee\quad\quad\left|\begin{array}{lcl}\begin{cases}y = -2 \\ x= -6\end{cases}\\\\\begin{cases}y=0 \\ x=4\end{cases}\end{array}\\ \right. \\ \\ \\\Rightarrow (x,y) =\Big\{(-6,-2);(-2,-6);(0,4);(4,0)\Big\}\\\\\text{(deoarece sistemul este simetric.)}[/tex]
