$\begin{equation*} \begin{cases} \frac{1}{3}x + \frac{1}{4}y - 2 = 0 |12 &\\ 5x - y = 11 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 4x + 3y - 24 = 0 &\\ 5x - y = 11 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 4x + 3y = 24 &\\ 5x - y = 11 |*3 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 4x + 3y = 24 &\\ 15x - 3y = 33 & \end{cases} \end{equation*}$
4x + 3y + 15x − 3y = 24 + 33
19x = 57
x = 3
5 * 3 − y = 11
15 − y = 11
y = 15 − 11
y = 4
Ответ: x = 3, y = 4.

$\begin{equation*} \begin{cases} 0,5x + 0,2y = 7 &\\ \frac{1}{3}x - \frac{1}{10}y = 0 |*30 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 0,5x + 0,2y = 7 |*15 &\\ 10x - 3y = 0 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 7,5x + 3y = 105 &\\ 10x - 3y = 0 & \end{cases} \end{equation*}$
7,5x + 3y + 10x − 3y = 105 + 0
17,5x = 105
x = 6
10 * 6 − 3y = 0
−3y = −60
y = 20
Ответ: x = 6, y = 20.

$\begin{equation*} \begin{cases} \frac{1}{5}m - \frac{1}{6}n = 0 |*30 &\\ 5m - 4n = 2 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 6m - 5n = 0 |*4 &\\ 5m - 4n = 2 |*5 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 24m - 20n = 0 &\\ 25m - 20n = 10 & \end{cases} \end{equation*}$
24m − 20n − (25m − 20n) = 0 − 10
24m − 20n − 25m + 20n = −10
−m = −10
m = 10
6 * 10 − 5n = 0
−5n = −60
n = 12
Ответ: n = 12, m = 10.

$\begin{equation*} \begin{cases} \frac{1}{6}u - \frac{1}{3}v = -3 |*6 &\\ 0,2u + 0,1v = 3,9 |*10 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} u - 2v = -18 |*2 &\\ 2u + v = 39 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 2u - 4v = -36 &\\ 2u + v = 39 & \end{cases} \end{equation*}$
2u − 4v − (2u + v) = −36 − 39
2u − 4v − 2u − v = −75
−5v = −75
v = 15
u − 2v = −18
u − 2 * 15 = −18
u = −18 + 30
u = 12
Ответ: v = 15, u = 12.