Ответ:

a = 1, b = 0, c = 1, d = -2

Объяснение:

[tex]\begin{equation*} \begin{cases} a + b + c + d = 0 \\ a + b - c - d = 2\\ a + c -b -d = 4\\ a + d - b - c = -2 \end{cases}\end{equation*}[/tex]

Прибавим к (2), (3), (4) первое уравнение (1):

[tex]\begin{equation*} \begin{cases} a + b + c + d = 0 \\ 2a +2b = 2\\ 2a + 2c = 4\\ 2a + 2d = -2 \end{cases}\end{equation*} \rightarrow \begin{equation*} \begin{cases} a + b + c + d = 0 \\ a +b = 1\\ a + c = 2\\ a + d = -1 \end{cases}\end{equation*} \rightarrow \begin{equation*} \begin{cases} a + b + c + d = 0 \\ b = 1 - a\\ c = 2-a\\ d = -1-a \end{cases}\end{equation*}[/tex]

Подставим в (1):

[tex]a + 1 - a + 2 - a - 1 - a = 0\\-2a + 2 = 0\\-2a = -2\\2a = 2\\a = 1[/tex]

Теперь найдем b,c,d:

[tex]\begin{equation*} \begin{cases} b = 1 - 1 = 0\\ c = 2-1 = 1\\ d = -1-1 = -2\end{cases}\end{equation*}[/tex]