The denominator of a fraction is $6$ more than the numerator. If $1$ is added to the numerator and $3$ is subtracted from the denominator,the fraction becomes $\frac{3}{4}$. Find the fraction.

It can take $12$ hours to fill a swimming pool using two pipes. If the pipe of larger diameter is used for $4$ hours and the pipe of smaller diameter for $9$ hours,only half the pool can be filled. How long would it take for each pipe to fill the pool separately?

Solve the following pair of linear equations:
$21x + 47y = 110$
$47x + 21y = 162$

In the pair of equations $a_{1}x + b_{1}y + c_{1} = 0$ and $a_{2}x + b_{2}y + c_{2} = 0$,if ............ then it has a unique solution.

Do the following pair of linear equations have no solution? Justify your answer.
$3x + y - 3 = 0$
$2x + \frac{2}{3}y = 2$

Solve the following pairs of equations:
$\frac{x}{3} + \frac{y}{4} = 4$
$\frac{5x}{6} - \frac{y}{8} = 4$