For a pair of equations $2x + 3y = 1$ and $3x - 2y = 8$,in usual notations $a_{1}b_{2} - a_{2}b_{1} = \dots$

Susan invested a certain amount of money in two schemes $A$ and $B,$ which offer interest at the rate of $8 \%$ per annum and $9 \%$ per annum,respectively. She received $Rs.\, 1860$ as annual interest. However,had she interchanged the amount of investments in the two schemes,she would have received $Rs.\, 20$ more as annual interest. How much money did she invest in each scheme?

Solve the following pair of linear equations:
$x + y = 3.3$
$\frac{0.6}{3x - 2y} = -1$,where $3x - 2y \neq 0$

$A$ person,rowing at the rate of $5 \, km/h$ in still water,takes thrice as much time in going $40 \, km$ upstream as in going $40 \, km$ downstream. Find the speed of the stream in $km/h$.

There are some $25$ paise coins and some $50$ paise coins in a bag. The total number of coins is $150$ and the amount in the bag is Rs. $55$. Find the number of coins of each value in the bag.

Solve the following pair of linear equations by the method of elimination:
$4x - 3y = 8$
$6x - y = \frac{29}{3}$