[tex]\displaystyle\bf\\\left \{ {{\sqrt{x} +\sqrt{y} =4} \atop {x-y=8}} \right. \\\\\\\left \{ {{\sqrt{x} +\sqrt{y} =4} \atop {(\sqrt{x} )^{2} -(\sqrt{y} )^{2} =8}} \right. \\\\\\\left \{ {{\sqrt{x} +\sqrt{y} =4} \atop {(\sqrt{x} -\sqrt{y} )(\sqrt{x}+ \sqrt{y} ) =8}} \right. \\\\\\\left \{ {{\sqrt{x} +\sqrt{y} =4} \atop {(\sqrt{x} -\sqrt{y} )\cdot 4 =8}} \right. \\\\\\+\left \{ {{\sqrt{x} +\sqrt{y} =4} \atop {\sqrt{x} -\sqrt{y} =2}} \right. \\----------\\2\sqrt{x} =6\\\\\sqrt{x} =3[/tex]

[tex]\displaystyle\bf\\x=9\\\\\\\sqrt{y} =4-\sqrt{x} =4-3=1\\\\y=1\\\\\\Otvet \ : \ \Big(9 \ ; \ 1\Big)[/tex]