1. Find the real tuple $(a, b, c, d)$ such that:
$$
\left\{\begin{array}{l}
a b+c+d=3, \\
b c+d+a=5, \\
c d+a+b=2, \\
d a+b+c=6 .
\end{array}\right.
$$
(2013, Dutch National Team Selection Exam)
提示 四个方程相加减后整理得
$$
(b-d)(a+c-2)=0 \text {. }
$$

进而解得 $(a, b, c, d)=(2,0,0,3)$.

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Hint: After adding and subtracting the four equations and simplifying, we get
$$
(b-d)(a+c-2)=0 \text {. }
$$

Thus, the solution is $(a, b, c, d)=(2,0,0,3)$.