For the linear equation in two variables $2x - 5y = 3$,if $y = -1$,then $x = \ldots$

$A$ fraction becomes $\frac{4}{5}$ if $1$ is added to both the numerator and the denominator. If $5$ is subtracted from both the numerator and the denominator,it becomes $\frac{1}{2}$. Find the fraction.

Are the following pair of linear equations consistent? Justify your answer.
$-3x - 4y = 12$
$3x + 4y = 12$

Solve the following pair of linear equations in two variables using a graph: $2x - 3y = 5$ and $4x - 6y = -13$.

Rajvansh invested some amount at the rate of $12 \%$ simple interest and some amount at the rate of $10 \%$ simple interest. He received a yearly interest of Rs. $130$. However,if he had interchanged the amounts invested,he would have received Rs. $4$ more as interest. How much amount did he invest at each rate?

Ankita travels $14 \,km$ to her home partly by rickshaw and partly by bus. She takes half an $hour$ if she travels $2 \,km$ by rickshaw and the remaining distance by bus. On the other hand,if she travels $4 \,km$ by rickshaw and the remaining distance by bus,she takes $9 \,minutes$ longer. Find the speed of the rickshaw and of the bus (in $km/h$).