$\begin{equation*} \begin{cases} y - 2x = 1 &\\ 6x - y = 7 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} y = 2x + 1 &\\ 6x - y = 7 & \end{cases} \end{equation*}$
6x − (2x + 1) = 7
6x − 2x − 1 = 7
4x = 7 + 1
4x = 8
x = 2
y = 2 * 2 + 1 = 4 + 1 = 5
Ответ: x = 2, y = 5.

$\begin{equation*} \begin{cases} 7x - 3y = 13 &\\ x - 2y = 5& \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 7x - 3y = 13 &\\ x = 2y + 5& \end{cases} \end{equation*}$
7(2y + 5) − 3y = 13
14y + 35 − 3y = 13
11y = 13 − 35
11y = −22
y = −2
x = 2 * (−2) + 5 = −4 + 5 = 1
Ответ: x = 1, y = −2.

$\begin{equation*} \begin{cases} x + y = 6 &\\ 3x - 5y = 2 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} y = 6 - x &\\ 3x - 5y = 2 & \end{cases} \end{equation*}$
3x − 5(6 − x) = 2
3x − 30 + 5x = 2
8x = 2 + 30
8x = 32
x = 4
y = 6 − x = 6 − 4 = 2
Ответ: x = 4, y = 2.

$\begin{equation*} \begin{cases} 4x - y = 11 &\\ 6x - 2y = 13& \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} y = 4x - 11 &\\ 6x - 2y = 13& \end{cases} \end{equation*}$
6x − 2(4x − 11) = 13
6x − 8x + 22 = 13
−2x = 13 − 22
−2x = −9
x = 4,5
y = 4 * 4,5 − 11 = 18 − 11 = 7
Ответ: x = 4,5, y = 7.

$\begin{equation*} \begin{cases} y - x = 20 &\\ 2x - 15y = -1 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} y = x + 20 &\\ 2x - 15y = -1 & \end{cases} \end{equation*}$
2x − 15(x + 20) = −1
2x − 15x − 300 = −1
−13x = −1 + 300
−13x = 299
x = −23
y = −23 + 20 = −3
Ответ: x = −23, y = −3.

$\begin{equation*} \begin{cases} 25 - x = -4y &\\ 3x - 2y = 30& \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} x = 25 + 4y &\\ 3x - 2y = 30& \end{cases} \end{equation*}$
3(25 + 4y) − 2y = 30
75 + 12y − 2y = 30
10y = 30 − 75
10y = −45
y = −4,5
x = 25 + 4y = 25 + 4 * (−4,5) = 25 − 18 = 7
Ответ: x = 7, y = −4,5.