Solve each of the following pairs of equations by reducing them to a pair of linear equations.

$\begin{array}{l}\frac{5}{x-1}+\frac{1}{y-2}=2\\ \frac{6}{x-1}-\frac{3}{y-2}=1\end{array}$

Solve each of the following pairs of equations by reducing them to a pair of linear equations.

$\begin{array}{cc}\frac{x+y}{xy} = & 2\\ \frac{x-y}{xy} = & 6\end{array}$

Solve each of the following pairs of equations by reducing them to a pair of linear equations.

$$\begin{gathered} \frac{2}{\sqrt{x}}+\frac{3}{\sqrt{y}}=2 \\ \frac{4}{\sqrt{x}}-\frac{9}{\sqrt{y}}=-1 \end{gathered}$$

Solve each of the following pairs of equations by reducing them to a pair of linear equations.

$$\begin{gathered} 6x+3y=6xy \\ 2x+4y=5xy \end{gathered}$$

Solve each of the following pairs of equations by reducing them to a pair of linear equations.

$\begin{array}{l}\frac{5}{x+y}-\frac{2}{x-y}=-1\\ \frac{15}{x+y}+\frac{7}{x-y}=10\end{array}$

Solve each of the following pairs of equations by reducing them to a pair of linear equations.

$$\begin{gathered} \frac{2}{x}+\frac{3}{y}=13 \\ \frac{5}{x}-\frac{4}{y}=-2 \end{gathered}$$

Solve each of the following pairs of equations by reducing them to a pair of linear equations.

$\begin{array}{l}\frac{10}{x+y}+\frac{2}{x-y}=4\\ \frac{15}{x+y}-\frac{5}{x-y}=-2\end{array}$

Solve each of the following pairs of equations by reducing them to a pair of linear equations.

$\begin{array}{l}\frac{1}{3x+y}+\frac{1}{3x-y}=\frac{3}{4}\\ \frac{1}{2(3x+y)}-\frac{1}{2(3x-y)}=\frac{-1}{8}\end{array}$

Formulate the following problems as a pair of equations and then find their solutions.

A boat goes $30 \mathrm{km}$ upstream and $44 \mathrm{km}$ downstream in $10$ hours. In $13$ hours it can go $40 \mathrm{km}$ upstream and $55 \mathrm{km}$ downstream. Determine the speed of the stream and that of the boat in still water.