Question

Find the general solution in positive integers, and the least values of $x$ and $y$ which satisfy the equations:
$17y-13x=0$.

Answer 1

$⟹$Let ${}^{\prime }{k}^{\prime }$ be a positive integer equal to ${}^{\prime }{x}^{\prime }:$
$\therefore y=\frac{13}{17}k$
${}^{\prime }{k}^{\prime }$ i.e., ${}^{\prime }{x}^{\prime }$ should be multiples of $17$ for $y$ to be positive.
Similarly, for $x$ to be positive, $y$ should be multiples of $13$.
$\therefore$ minimum value of $x$ $=17$
minimum value of $y$ $=13$