$\begin{equation*} \begin{cases} \frac{1}{2}x - \frac{1}{3}y = 1 | * (-12) &\\ 6x - 5y = 3 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} -6x + 4y = -12 &\\ 6x - 5y = 3 & \end{cases} \end{equation*}$
−6x + 4y + 6x − 5y = −12 + 3
−y = −9
y = 9
6x − 5y = 3
6x = 3 + 5y
6x = 3 + 5 * 9
6x = 3 + 45
6x = 48
x = 48 : 6
x = 8
Ответ: (8;9)

$\begin{equation*} \begin{cases} \frac{1}{3}x + \frac{1}{5}y = 11 | * 10 &\\ \frac{3}{5}x - 2y = 8 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} \frac{10}{3}x + 2y = 110 &\\ \frac{3}{5}x - 2y = 8 & \end{cases} \end{equation*}$
$\frac{10}{3}x + 2y + \frac{3}{5}x - 2y = 110 + 8$
$\frac{50 + 9}{15}x = 118$
$\frac{59}{15}x = 118$
$x = 118 : \frac{59}{15}$
$x = 118 * \frac{15}{59}$
x = 2 * 15
x = 30
$\frac{3}{5}x - 2y = 8$
$2y = \frac{3}{5}x - 8$
$2y = \frac{3}{5} * 30 - 8$
2y = 6 * 3 − 8
2y = 18 − 8
2y = 10
y = 10 : 2
y = 5
Ответ: (30;5)

$\begin{equation*} \begin{cases} \frac{1}{4}x - \frac{1}{3}y = 4 * (-9) &\\ \frac{4}{5}x - 3y = 7 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} -\frac{9}{4}x + 3y = -36 &\\ \frac{4}{5}x - 3y = 7 & \end{cases} \end{equation*}$
$-\frac{9}{4}x + 3y + \frac{4}{5}x - 3y = -36 + 7$
$\frac{-45 + 16}{20}x = -29$
$-\frac{29}{20}x = -29$
$x = -29 : (-\frac{29}{20})$
$x = -29 * (-\frac{20}{29})$
x = 20
$\frac{4}{5}x - 3y = 7$
$3y = \frac{4}{5}x - 7$
$3y = \frac{4}{5} * 20 - 7$
3y = 4 * 4 − 7
3y = 16 − 7
3y = 9
y = 9 : 3
y = 3
Ответ: (20;3)

$\begin{equation*} \begin{cases} \frac{1}{5}x + \frac{1}{4}y = -1 | * (-10) &\\ 2x - 3y = -54 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} -2x - 2,5y = 10 &\\ 2x - 3y = -54 & \end{cases} \end{equation*}$
−2x − 2,5y + 2x − 3y = 10 − 54
−5,5 = −44
y = −44 : (−5,5)
y = 8
2x − 3y = −54
2x = −54 + 3y
2x = −54 + 3 * 8
2x = −54 + 24
2x = −30
x = −30 : 2
x = −15
Ответ: (−15;8)