ÖMO 1997 Problem 1

Let $a$ be a fixed integer. Find all integer solutions $x, y, z$ of the system $$5x + (a + 2)y + (a + 2)z = a,$$$$(2a + 4)x + (a^2 + 3)y + (2a + 2)z = 3a - 1,$$$$(2a + 4)x + (2a + 2)y + (a^2 + 3)z = a + 1.$$