$59)\left\{\begin{matrix} x^{2}+3y\sqrt{\frac{x^{2}-1}{y}}=1+4y & \\ \sqrt[3]{x+6}+\sqrt{x+y-x^{2}}=y& \end{matrix}\right.$
$60)\left\{\begin{matrix} \sqrt{3x+y}+\sqrt{2x+7y} =10& \\ (\sqrt{x}+\sqrt{y})(\frac{1}{\sqrt{x+3y}}+\frac{1}{\sqrt{3x+y}})=2& \end{matrix}\right.$
$61)\left\{\begin{matrix} x\sqrt{y}+y\sqrt{x}+2(x+y-xy)=4 & \\ x\sqrt{x^{2}+3xy}+y\sqrt{y^{2}+3xy}=4& \end{matrix}\right.$
$62)\left\{\begin{matrix} xy+6y\sqrt{x-1}+12y=4 & \\ \frac{xy}{1+y}+\frac{1}{xy+y}=\frac{2\sqrt{x}}{\sqrt{x}+\sqrt{y}}& \end{matrix}\right.$
$63)\left\{\begin{matrix} 9y^{2}(x+3y)=1-x^{3}y^{3} & \\ \sqrt{x^{2}+1}=y+2\sqrt{2} & \end{matrix}\right.$
$64)(x+1)\sqrt{x+2}+(x+6)\sqrt{x+7}=x^{2}+7x+12$