Solve the following pair of equations by the method of cross-multiplication:
$x + 2y + 1 = 0$
$2x - 3y - 12 = 0$

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.

For the pair of equations $\frac{2}{x} + \frac{3}{y} = 3$ and $\frac{3}{x} + \frac{2}{y} = 7$,find the value of $\frac{3}{x} + \frac{3}{y}$.

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

The cost of $5$ pants and $8$ shirts is ₹ $3100$. If the cost of a pant is ₹ $x$ and a shirt is ₹ $y$,then the linear equation in two variables is:

The denominator of a fraction is $6$ more than the numerator. If $1$ is added to the numerator and $3$ is subtracted from the denominator,the fraction becomes $\frac{3}{4}$. Find the fraction.