2015 Algebra #10: Contrived System of Equations
Source:
March 28, 2015
algebrasystem of equations
Problem Statement
Find all ordered 4-tuples of integers (not necessarily distinct) satisfying the following system of equations: \begin{align*}a^2-b^2-c^2-d^2&=c-b-2\\2ab&=a-d-32\\2ac&=28-a-d\\2ad&=b+c+31.\end{align*}