Exercise 3.6

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

$\frac{4}{x}+3y=14$

$\frac{3}{x}-4y=23$

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

$\frac{5}{x-1}+\frac{1}{y-2}=2$

$\frac{6}{x-1}-\frac{3}{y-2}=1$

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

$\frac{7x-2y}{xy}=5$

$\frac{8x+7y}{xy}=15$

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

$6x+3y=6xy$

$2x+4y=5xy$

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

$\frac{10}{x+y}+\frac{2}{x-y}=4$

$\frac{15}{x+y}-\frac{5}{x-y}=-2$

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

$\frac{1}{3x+y}+\frac{1}{3x-y}=\frac{3}{4}$

$\frac{1}{2\left(3x+y\right)}-\frac{1}{2\left(3x-y\right)}=\frac{-1}{8}$

$2$ women and $5$ men can together finish an embroidery work in $4$ days, while $3$ women and 6 men can finish it in $3$ days. Find the time taken by $1$ woman alone to finish the work, and also the time taken by $1$ man alone.

Formulate the following problem as a pair of equations, and hence find their solution.

Roohi travels $300 \mathrm{k}\mathrm{m}$ to her home partly by train and partly by bus. She takes $4$ hours if she travels $60 \mathrm{k}\mathrm{m}$ by train and the remaining by bus. If she travels $100 \mathrm{k}\mathrm{m}$ by train and the remaining by bus, she takes $10$ minutes longer. Find the speed of the train and the bus separately.