The standard form of the equation $3x = 2y - 1$ is..........

In a rectangle,the length is $3$ less than twice its width. The perimeter of the rectangle is $100$. Represent this situation as a pair of linear equations in two variables.

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

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.

Solve the following pair of linear equations in two variables using the graphical method: $2x + y = 7$ and $x - 2y = 6$.

Write an equation of a line passing through the point representing the solution of the pair of linear equations $x+y=2$ and $2x-y=1$. How many such lines can we find?