For a pair of equations $13x - 7y = 19$ and $7x - 13y = 31$,find the value of $x + y$.

Pathik travels $600 \, km$ to his home partly by train and partly by car. He takes $8$ hours if he travels $120 \, km$ by train and the rest by car. He takes $20$ minutes longer if he travels $200 \, km$ by train and the rest by car. Find the speed of the train and the car.

Determine,graphically,the vertices of the triangle formed by the lines $y=x$,$3y=x$,and $x+y=8$.

Solve the following pair of linear equations in two variables using a graph: $x + y = 8$ and $x - y = 2$.

Vijay had some bananas,and he divided them into two lots $A$ and $B$. He sold the first lot at the rate of $Rs. 2$ for $3$ bananas and the second lot at the rate of $Rs. 1$ per banana,and got a total of $Rs. 400$. If he had sold the first lot at the rate of $Rs. 1$ per banana,and the second lot at the rate of $Rs. 4$ for $5$ bananas,his total collection would have been $Rs. 460$. Find the total number of bananas he had.

Do the following equations represent a pair of coincident lines? Justify your answer.
$3x + \frac{1}{7}y = 3$
$7x + 3y = 7$