Factorization Techniques

$x+8y$ and $x-3y$ are factors of $12$, which are $\pm1,\pm2,\pm3,\pm4,\pm6,\pm12$.

so their difference is a multiple of $11$.

$x+9$ and $y+14$ are factors of $187$.

The divisors of $187$ are $\pm1,\pm11,\pm17,\pm187$.

$x$ and $y$ are in the denominator, so they cannot be zero.

Find $x$ and $y$ in integers such that