Akhila went to a fair in her village. She wanted to enjoy rides in the Giant Wheel and play Hoopla (a game in which you throw a rig on the items kept in the stall, and if the ring covers any object completely you get it.) The number of times she played Hoopla is half the number of rides she had on the Giant Wheel. Each ride costs $₹3,$ and a game of Hoopla costs $₹4.$ If she spent $₹20$ in the fair, represent this situation algebraically and graphically.

Check graphically whether the pair of equations

$x+3y=6$ .....(1)

and 

$2x-3y=12$ .....(2)

is consistent. If so, solve them graphically

Find whether the following pair of equations has no solution, unique solution or infinitely many solutions:

$5x-8y+1=0 \left(1\right)$

$3x-\frac{24}{5}y+\frac{3}{5}=0 \left(2\right)$

Solve the following pair of equations by substitution method:

$7x-15y=2 \left(1\right)$

$x+2y=3 \left(2\right)$

Aftab tells his daughter, "Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be." Solve this by the method of substitution.

The cost of $2$ pencils and $3$ erasers is $₹9$ and the cost of $4$ pencils and $6$ erasers is $₹18$. Find the cost of each pencil and each eraser.