1)\(\begin{cases}\sqrt{4x^2+\left(4x-9\right)\left(x-3y\right)}+\sqrt{3xy}=9y\\4\sqrt{\left(x+2\right)\left(3y+2x\right)}=3x+9\end{cases}\) 4)\(\begin{cases}\left(x^2+y\right)\sqrt{x-y+6}=2x^2-x+3y-2\\\sqrt{10x-xy-12}+1=\frac{y-x}{\sqrt{y-4}+\sqrt{6-x}}\end{cases}\)
2)\(\begin{cases}x^2+\left(y-6\right)^2=y+13x+27\\\sqrt{9x^2+\left(2x-3\right)\left(x-y\right)}+4\sqrt{xy}=7y\end{cases}\) 5)\(\begin{cases}\sqrt{4xy+\left(3\sqrt{xy}-7\right)\left(x-y\right)}+2\sqrt{xy}=4y\\\left(2x+1\right)\left[12y-1+9\sqrt{xy}-x^2-x\right]=27\left(x+1\right)\end{cases}\)
3)\(\begin{cases}\sqrt{\left(x+2\right)\left(y+1\right)+\left(x-y+1\right)\sqrt{y^2+1}}+\sqrt{x+2}=y+\sqrt{y+1}+1\\\sqrt{3x+1}-\sqrt{y+1}=2x^2+4x-y-1\end{cases}\)
