The solution of the pair of equations $x + 2y = 5$ and $3x + 5y = 13$ is ...........

The total cost of $3 \,kg$ of mangoes and $1 \,kg$ of pomegranate is Rs. $200$,and the total cost of $1 \,kg$ of mango and $1 \,kg$ of pomegranate is Rs. $80$. Represent this situation as a pair of linear equations in two variables.

Solve the following pair of equations by the method of elimination:
$11x + 13y = 61$
$13x + 11y = 59$

$A$ shopkeeper sells a saree at $8 \%$ profit and a sweater at $10 \%$ discount,thereby,getting a sum of $Rs. 1008$. If she had sold the saree at $10 \%$ profit and the sweater at $8 \%$ discount,she would have got $Rs. 1028$. Find the cost price of the saree and the list price (price before discount) of the sweater (in $Rs.$).

In a rectangle,the length is $3$ less than twice its width. The perimeter of the rectangle is $100$. Represent this situation as a pair of linear equations in two variables.

Solve the pair of linear equations $2x + y = 40$ and $x + y = 30$. If the solution satisfies the equation $y = mx + 6$,find the value of $m$.