Solving the first equation 14XX + 27X = 656:

14X^2 + 27X - 656 = 0

Factoring the quadratic equation, we get:

(2X - 41)(7X + 16) = 0

So, X = 41/2 or X = -16/7

Solving the second equation 81y - 38y = 645:

43y = 645

y = 645 / 43

y = 15

Therefore, the solutions to the equations are:

X = 41/2 or X = -16/7
y = 15