$\begin{equation*} \begin{cases} x - y = -1 &\\ y - z = -1 &\\ z + x = 8 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} y = x + 1 &\\ y - z = -1 &\\ z = 8 - x & \end{cases} \end{equation*}$
y − z = −1
x + 1 − (8 − x) = −1
x + 1 − 8 + x = −1
2x = −1 − 1 + 8
2x = 6
x = 3
y = x + 1 = 3 + 1 = 4
z = 8 − x = 8 − 3 = 5
Ответ: x = 3, y = 4, z = 5.

$\begin{equation*} \begin{cases} x + y = -3 &\\ y + z = 6 &\\ z + x = 1 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} y = -3 - x &\\ y + z = 6 &\\ z = 1 - x & \end{cases} \end{equation*}$
y + z = 6
−3 − x + 1 − x = 6
−2x = 6 + 3 − 1
−2x = 8
x = −4
y = −3 − x = −3 − (−4) = −3 + 4 = 1
z = 1 − x = 1 − (−4) = 1 + 4 = 5
Ответ: x = −4, y = 1, z = 5.

$\begin{equation*} \begin{cases} x - y + 2z = 1 &\\ x - y - z = -2 &\\ 2x - y + z = -1 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} x - y = 1 - 2z &\\ (x - y) - z = -2 &\\ 2x - y + z = -1 & \end{cases} \end{equation*}$
(x − y) − z = −2
1 − 2z − z = −2
−3z = −2 − 1
−3z = −3
z = 1
$\begin{equation*} \begin{cases} x - y = 1 - 2 &\\ z = 1 &\\ 2x - y + 1 = -1 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} x - y = -1 &\\ z = 1 &\\ 2x - y = -2 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} y = x + 1 &\\ z = 1 &\\ 2x - y = -2 & \end{cases} \end{equation*}$
2x − y = −2
2x − (x + 1) = −2
2x − x − 1 = −2
x = −2 + 1
x = −1
y = x + 1 = −1 + 1 = 0
Ответ: x = −1, y = 0, z = 1.