$\begin{equation*} \begin{cases} \frac{1}{3}x - \frac{1}{12}y = 4 |*12 &\\ 6x + 5y = 150 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 4x - y = 48 |*5 &\\ 6x + 5y = 150 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 20x - 5y = 240 &\\ 6x + 5y = 150 & \end{cases} \end{equation*}$
20x − 5y + 6x + 5y = 240 + 150
26x = 390
x = 15
4 * 15 − y = 48
60 − y = 48
y = 60 − 48
y = 12
Ответ: x = 15, y = 12.

$\begin{equation*} \begin{cases} \frac{1}{3}v - \frac{1}{8}u = 3 |*24 &\\ 7u + 9v = -2 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 8v - 3u = 72 |*7 &\\ 7u + 9v = -2 |*3 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 56v - 21u = 504 &\\ 21u + 27v = -6 & \end{cases} \end{equation*}$
56v − 21u + 21u + 27v = 504 − 6
83v = 498
v = 6
7u + 9 * 6 = −2
7u = −2 − 54
7u = −56
u = −8
Ответ: v = 6, u = −8.

$\begin{equation*} \begin{cases} \frac{x}{4} + \frac{y}{6} = 1 |*12 &\\ 2x + 3y = -12 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 3x + 2y = 12 |*3 &\\ 2x + 3y = -12 |*2 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 9x + 6y = 36 &\\ 4x + 6y = -24 & \end{cases} \end{equation*}$
9x + 6y − (4x + 6y) = 36 − (−24)
9x + 6y − 4x − 6y = 36 + 24
5x = 60
x = 12
2 * 12 + 3y = −12
3y = −12 − 24
3y = −36
y = −12
Ответ: x = 12, y = −12.

$\begin{equation*} \begin{cases} 4a - 5b - 10 = 0 &\\ \frac{a}{5} - \frac{b}{3} + \frac{1}{3} = 0 |*15 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 4a - 5b - 10 = 0 &\\ 3a - 5b + 5 = 0 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 4a - 5b = 10 &\\ 3a - 5b = -5 & \end{cases} \end{equation*}$
4a − 5b − (3a − 5b) = 10 − (−5)
4a − 5b − 3a + 5b = 10 + 5
a = 15
3 * 15 − 5b = −5
−5b = −5 − 45
−5b = −50
b = 10
Ответ: a = 15, b = 10.