$\begin{equation*} \begin{cases} 12x - 7y = 2 &\\ 4x - 5y = 6 |*3 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 12x - 7y = 2 &\\ 12x - 15y = 18 & \end{cases} \end{equation*}$
12x − 7y − (12x − 15y) = 2 − 18
12x − 7y − 12x + 15y = −16
8y = −16
y = −2
4x − 5y = 6
4x − 5 * (−2) = 6
4x + 10 = 6
4x = 6 − 10
4x = −4
x = −1
Ответ: x = −1, y = −2.

$\begin{equation*} \begin{cases} 7u + 2v = 1 |*3 &\\ 17u + 6v = -9 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 21u + 6v = 3 &\\ 17u + 6v = -9 & \end{cases} \end{equation*}$
21u + 6v − (17u + 6v) = 3 − (−9)
21u + 6v − 17u − 6v = 3 + 9
4u = 12
u = 3
7 * 3 + 2v = 1
2v = 1 − 21
2v = −20
v = −10
Ответ: u = 3, v = −10.

$\begin{equation*} \begin{cases} 6x = 25y + 1 &\\ 5x - 16y = -4 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 6x - 25y = 1 |*5 &\\ 5x - 16y = -4 |*6 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 30x - 125y = 5 &\\ 30x - 96y = -24 & \end{cases} \end{equation*}$
30x − 125y − (30x − 96y) = 5 − (−24)
30x − 125y − 30x + 96y = 5 + 24
−29y = 29
y = −1
6x − 25 * (−1) = 1
6x + 25 = 1
6x = 1 − 25
6x = −24
x = −4
Ответ: x = −4, y = −1.

$\begin{equation*} \begin{cases} 4b + 7a = 90 |*3 &\\ 5a - 6b = 20 |*2 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 12b + 21a = 270 &\\ 10a - 12b = 40 & \end{cases} \end{equation*}$
12b + 21a + 10a − 12b = 270 + 40
31a = 310
a = 10
5 * 10 − 6b = 20
−6b = 20 − 50
−6b = −30
b = 5
Ответ: a = 10, b = 5.