Question 60
Find all combinations of four integers $(a, b, c, d)$ satisfying the equations
$$
\begin{cases} -a^2 + b^2 + c^2 + d^2 = 1 \\ 3a + b + c + d = 1. \end{cases}
$$
$$
\begin{cases} -a^2 + b^2 + c^2 + d^2 = 1 \\ 3a + b + c + d = 1. \end{cases}
$$