Find the values of $x$ and $y$ in the following rectangle.

$A$ pair of linear equations which has a unique solution $x=2, y=-3$ is

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 equations: $2x + y = \frac{7xy}{3}, x + 3y = \frac{11xy}{3}$

Are the following pair of linear equations consistent? Justify your answer.
$2ax + by = a$
$4ax + 2by - 2a = 0$; $a, b \neq 0$

If $\frac{x}{2} = \frac{6}{y} = 3$,then $x + y = \ldots$