12.5.6 Olympic Algebra

Condition: Solve in positive integers \ (x, y, z \) the system of equations: \ [\ left \ {\ begin {array} {l} {1} -20 y+15 z = 18 \\ \ frac {1} -15 z+18 z+18 z+18 x = 20 \\ \ frac {1} {z} -18 x+20 y = 15 \ end {Array} \ Right. \]