Помогите пожалуйста решить

$\left \{ {{log_2 x+ \frac{1}{2}log_2 \frac{1}{y}=4} \atop {xy=2}} \right.$
ОДЗ: $x\ \textgreater \ 0;y \neq 0;y\ \textgreater \ 0$
$\left \{ {{log_2 \frac{x}{ \sqrt{y} }=log_2 16} \atop {xy=2}} \right.$
$\left \{ {{\frac{x}{ \sqrt{y} }= 16} \atop {xy=2}} \right.$
$\left \{ {{x= 16\sqrt{y}} \atop {xy=2}} \right.$
$\left \{ {{x= 16\sqrt{y}} \atop {16\sqrt{y}*y=2}} \right.$
$\left \{ {{x= 16\sqrt{y}} \atop {y^{ \frac{3}{2} }= \frac{1}{8} }} \right.$
$\left \{ {{x= 16\sqrt{y}} \atop {y^{ \frac{3}{2} }=2^{-3} }} \right.$
$\left \{ {{x= 16\sqrt{y}} \atop {y=(2^{-3})^{ \frac{2}{3} } }} \right.$
$\left \{ {{x= 16\sqrt{y}} \atop {y=2^{-2} }} \right.$
$\left \{ {{x= 16\sqrt{y}} \atop {y= \frac{1}{4} }} \right.$
$\left \{ {{x= 16\sqrt{ \frac{1}{4} }} \atop {y= \frac{1}{4} }} \right.$
$\left \{ {{x= 16* \frac{1}{2} } \atop {y= \frac{1}{4} }} \right.$
$\left \{ {{x= 8} \atop {y= \frac{1}{4} }} \right.$