ISL 1988 Problem 62

Let $x = p, y = q, z = r, w = s$ be the unique solution of the system of linear equations $$x + a_i \cdot y + a^2_i \cdot z + a^3_i \cdot w = a^4_i, i = 1,2,3,4.$$ Express the solutions of the following system in terms of $p,q,r$ and $s:$ $$x + a^2_i \cdot y + a^4_i \cdot z + a^6_i \cdot w = a^8_i, i = 1,2,3,4.$$ Assume the uniquness of the solution.