\(2,\Leftrightarrow\left\{{}\begin{matrix}20x+25y-10xy=0\\20x-30y+xy=0\end{matrix}\right.\Leftrightarrow55y-11xy=0\\ \Leftrightarrow11y\left(5-x\right)=0\Leftrightarrow\left[{}\begin{matrix}y=0\\x=5\end{matrix}\right.\)

Với \(y=0\Leftrightarrow4x+0=0\Leftrightarrow x=0\)

Với \(x=5\Leftrightarrow20+5y=10y\Leftrightarrow y=4\)

Vậy \(\left(x;y\right)=\left\{\left(0;0\right);\left(5;4\right)\right\}\)

1: ĐKXĐ: x<>0; y<>0

\(\begin{cases}\frac{5}{12y}+\frac{1}{4x}=\frac{4}{3xy}\\ \frac{1}{3y}-\frac{3}{4x}=\frac{47}{12xy}\end{cases}\Rightarrow\begin{cases}\frac{5x}{12xy}+\frac{3y}{12xy}=\frac{16}{12xy}\\ \frac{4x}{12xy}-\frac{9y}{12xy}=\frac{47}{12xy}\end{cases}\)

=>\(\begin{cases}5x+3y=16\\ 4x-9y=47\end{cases}\Rightarrow\begin{cases}15x+9y=48\\ 4x-9y=47\end{cases}\)

=>\(\begin{cases}15x+9y+4x-9y=48+47\\ 4x-9y=47\end{cases}\Rightarrow\begin{cases}19x=95\\ 9y=4x-47\end{cases}\)

=>\(\begin{cases}x=5\\ 9y=4\cdot5-47=20-47=-27\end{cases}\Rightarrow\begin{cases}x=5\\ y=-3\end{cases}\) (nhận)

2: \(\begin{cases}4x+5y=2xy\\ 20x-30y+xy=0\end{cases}\Rightarrow\begin{cases}4x+5y=2xy\\ 20x-30y=-xy\end{cases}\)

=>\(\begin{cases}4x+5y=2xy\\ 40x-60y=-2xy\end{cases}\Rightarrow\begin{cases}4x+5y+40x-60y=0\\ 4x+5y=2xy\end{cases}\)

=>\(\begin{cases}44x-55y=0\\ 4x+5y=2xy\end{cases}\Rightarrow\begin{cases}4x=5y\\ 4x+5y=2xy\end{cases}\)

=>\(\begin{cases}x=1,25y\\ 10y=2xy\end{cases}\Rightarrow\begin{cases}x=1,25y\\ 10y=2y\cdot1,25y=2,5y^2\end{cases}\)

=>\(\begin{cases}x=1,25y\\ y^2=4y\end{cases}\Rightarrow\begin{cases}x=1,25y\\ y\left(y-4\right)=0\end{cases}\)

TH1: y=0

=>\(x=1,25\cdot0=0\)

TH2: y-4=0

=>y=4

=>\(x=1,25\cdot4=5\)

3: \(\begin{cases}\frac{2x+y}{5}=4+\frac{y}{2}\\ \frac{2\left(1-x\right)}{y+2}=2-\frac{x+1}{y+2}\end{cases}\Rightarrow\begin{cases}\frac{2\left(2x+y\right)}{10}=\frac{40}{10}+\frac{5y}{10}\\ \frac{2\left(1-x\right)}{y+2}=\frac{2y+4-x-1}{y+2}\end{cases}\)

=>\(\begin{cases}2\left(2x+y\right)=5y+40\\ 2\left(1-x\right)=2y-x+3\end{cases}\Rightarrow\begin{cases}4x+2y=5y+40\\ 2-2x-2y+x-3=0\end{cases}\)

=>\(\begin{cases}4x-3y=30\\ -x-2y-1=0\end{cases}\Rightarrow\begin{cases}4x-3y=30\\ x+2y=-1\end{cases}\)

=>\(\begin{cases}4x-3y=30\\ 4x+8y=-4\end{cases}\Rightarrow\begin{cases}4x-3y-4x-8y=30+4\\ x+2y=-1\end{cases}\)

=>\(\begin{cases}-11y=34\\ x+2y=-1\end{cases}\Rightarrow\begin{cases}y=-\frac{34}{11}\\ x=-1-2y=-1-2\cdot\frac{-34}{11}=-1+\frac{68}{11}=\frac{-11+68}{11}=\frac{57}{11}\end{cases}\)

4: ĐKXĐ: x>0; y>0

\(\begin{cases}\frac{4}{\sqrt{x}}+\frac{3}{\sqrt{y}}=\frac{13}{36}\\ \frac{6}{\sqrt{x}}+\frac{10}{\sqrt{y}}=1\end{cases}\Rightarrow\begin{cases}\frac{12}{\sqrt{x}}+\frac{9}{\sqrt{y}}=\frac{13}{12}\\ \frac{12}{\sqrt{x}}+\frac{20}{\sqrt{y}}=2\end{cases}\)

=>\(\begin{cases}\frac{12}{\sqrt{x}}+\frac{20}{\sqrt{y}}-\frac{12}{\sqrt{x}}-\frac{9}{\sqrt{y}}=2-\frac{13}{12}\\ \frac{6}{\sqrt{x}}+\frac{10}{\sqrt{y}}=1\end{cases}\Rightarrow\begin{cases}\frac{11}{\sqrt{y}}=\frac{11}{12}\\ \frac{6}{\sqrt{x}}=1-\frac{10}{\sqrt{y}}\end{cases}\)

=>\(\begin{cases}\sqrt{y}=12\\ \frac{6}{\sqrt{x}}=1-\frac{10}{12}=\frac{12}{12}-\frac{10}{12}=\frac{2}{12}=\frac16\end{cases}\Rightarrow\begin{cases}y=144\\ \sqrt{x}=6\cdot6=36\end{cases}\)

=>y=144(nhận) và x=1296(nhận)