For eliminating $y$ from the equations $3x - 2y = 1$ and $5x + y = 6$,the second equation should be multiplied by

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.

Solve the following pairs of equations:
$\frac{x}{3} + \frac{y}{4} = 4$
$\frac{5x}{6} - \frac{y}{8} = 4$

Do the equations $4x + 3y - 1 = 5$ and $12x + 9y = 15$ represent a pair of coincident lines? Justify your answer.

$A$ 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 $Rs.$).

For a pair of equations $9x - 4y = 14$ and $7x - 3y = 11$,find the value of $y$.