I'm looking for solutions to the non-linear system of equations $$ n_1x + (n_1 - 1)y = a_1 \\ n_2x + (n_2 - 1)y = a_2 \\ n_3x + (n_3 - 1)y = a_3 \\ n_4x + (n_4 - 1)y = a_4 $$ where $x$ and $y$ are positive rational numbers, $(n_i)$ are positive integers and $(a_i)$ are known positive rational constants. Any clues?
Geometrically, this can be interpreted as determining the length $x$ of an object so that when placing $n_i$ instances of the object after one another with a distance of $y$ between each object they will add up to a total length of $a_i$.