The ages of two girls are in the ratio $5:7$. Eight years ago,their ages were in the ratio $7:13$. Represent this situation as a pair of linear equations in two variables.

(N/A) Suppose the present age of the first girl is $x$ years and the present age of the second girl is $y$ years.
The ratio of their present ages is $x:y = 5:7$.
This implies $\frac{x}{y} = \frac{5}{7}$,which simplifies to $7x = 5y$ or $7x - 5y = 0$ ......... $(1)$
Eight years ago,the age of the first girl was $(x - 8)$ years and the age of the second girl was $(y - 8)$ years.
The ratio of their ages eight years ago was $(x - 8) : (y - 8) = 7 : 13$.
This implies $\frac{x - 8}{y - 8} = \frac{7}{13}$.
Cross-multiplying gives $13(x - 8) = 7(y - 8)$.
$13x - 104 = 7y - 56$.
$13x - 7y = 104 - 56$.
$13x - 7y = 48$ ......... $(2)$
Thus,the pair of linear equations representing the situation is $7x - 5y = 0$ and $13x - 7y = 48$.