Two straight paths are represented by the equations $x-3y=2$ and $-2x+6y=5$. Check whether the paths cross each other or not.

The graph of the pair of equations $x+y=7$ and $3x+3y=21$ is:

For a pair of equations,if $a_{1} b_{2}-a_{2} b_{1}=0, b_{1} c_{2}-b_{2} c_{1}=0$ and $c_{1} a_{2}-c_{2} a_{1}=0$,then the solution set of the pair of equations is ...........

If $y = \frac{1}{2} x$ and $x + 2y = 8$,then $x = \dots$

Ankita travels $14 \,km$ to her home partly by rickshaw and partly by bus. She takes half an $hour$ if she travels $2 \,km$ by rickshaw and the remaining distance by bus. On the other hand,if she travels $4 \,km$ by rickshaw and the remaining distance by bus,she takes $9 \,minutes$ longer. Find the speed of the rickshaw and of the bus (in $km/h$).

Which of the following groups matches the data of Part $I$ with the data of Part $II$?

Part $I$	Part $II$
$1. x+2y=3, 2x+4y=5$	$a. \text{Solution set is a singleton set.}$
$2. 2x+3y=6, x+\frac{3}{2}y=3$	$b. \text{Solution set is an empty set.}$
$3. 3x-y=0, x-y+6=0$	$c. \text{Solution set is an infinite set.}$
	$d. \text{Solution set contains two members.}$