Solve the following pair of linear equations by the method of substitution: $3x + y + 1 = 0$ and $2x - 3y + 8 = 0$.

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

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

The total cost of $7$ pens and $5$ pencils is Rs. $50$,and the total cost of $5$ pens and $7$ pencils is Rs. $46$. Represent this as a pair of linear equations in two variables.

Jamila sold a table and a chair for $Rs.\, 1050,$ thereby making a profit of $10\%$ on the table and $25\%$ on the chair. If she had taken a profit of $25\%$ on the table and $10\%$ on the chair,she would have got $Rs.\, 1065.$ Find the cost price of each (in $Rs.$).

The cost of $2\,kg$ of apples and $1\,kg$ of grapes on a day was found to be Rs. $160$. After a month,the cost of $4\,kg$ of apples and $2\,kg$ of grapes is Rs. $300$. Represent this situation as a pair of linear equations in two variables.

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 ...........