$A$ fraction becomes $\frac{1}{4}$ if $2$ is subtracted from the numerator and $3$ is added to the denominator. If $6$ is added to the numerator and the denominator is multiplied by $3$,it becomes $\frac{2}{3}$. Find the fraction.

In the pair of equations $a_{1}x + b_{1}y + c_{1} = 0$ and $a_{2}x + b_{2}y + c_{2} = 0$,if ............ then it has a unique solution.

Solve the following pair of linear equations in two variables using the graphical method: $y + x = 5$ and $y - x = 9$.

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?

Naresh has double the money that Yogesh has. If Naresh gives Yogesh ₹ $20$,then both have equal money. The pair of equations obtained from this data is $\ldots \ldots \ldots \ldots .$

The solution of the pair of equations $x + 2y = 5$ and $3x + 5y = 13$ is ...........