Решите систему уравнений Корень из х+корень из у=3 ху=4

Решите задачу:

$\left \{ {{ \sqrt{x} + \sqrt{y}=3} \atop {xy=4}} \right. \left \{ {{ \sqrt{x+y} =2} \atop { xy=4}} \right. \left \{ {{x+y=4} \atop {xy=4}} \right. \left \{ {{x=4-y} \atop {(4-y)y=4}} \right. \left \{ {{x=4-2} \atop {y=2}} \right. \left \{ {{x=2} \atop {y=2}} \right.$
$(4-y)y=4$
$\left \{ {{4-y=2} \atop {y=2}} \right. \left \{ {{y=2} \atop {y=2}} \right.$