On comparing the ratios $\frac{a_{1}}{a_{2}}, \frac{b_{1}}{b_{2}}$ and $\frac{c_{1}}{c_{2}},$ find out whether the following pair of linear equations are consistent or inconsistent.
$5x - 3y = 11$; $-10x + 6y = -22$

Check graphically whether the pair of equations
$x+3y=6$ $...(1)$
and $2x-3y=12$ $...(2)$
is consistent. If so,solve them graphically.

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

Solve the following pair of equations by reducing them to a pair of linear equations:
$\frac{5}{x-1} + \frac{1}{y-2} = 2$
$\frac{6}{x-1} - \frac{3}{y-2} = 1$

Formulate the following problems as a pair of equations,and hence find their solutions:
Roohi travels $300 \ km$ to her home partly by train and partly by bus. She takes $4 \ hours$ if she travels $60 \ km$ by train and the remaining by bus. If she travels $100 \ km$ by train and the remaining by bus,she takes $10 \ minutes$ longer. Find the speed of the train and the bus separately.

Use the elimination method to find all possible solutions of the following pair of linear equations:
$2x + 3y = 8$ $...(1)$
$4x + 6y = 7$ $...(2)$