Question 8
The real numbers $a, b, c, d$ satisfy simultaneously the equations
$$
abc - d = 1, \quad bcd - a = 2, \quad cda - b = 3, \quad dab - c = -6.
$$
Prove that $a + b + c + d \neq 0$.
$$
abc - d = 1, \quad bcd - a = 2, \quad cda - b = 3, \quad dab - c = -6.
$$
Prove that $a + b + c + d \neq 0$.