$\begin{equation*} \begin{cases} \frac{x}{5} = 1 - \frac{y}{15} |*15 &\\ 2x - 5y = 0 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 3x = 15 - y &\\ 2x - 5y = 0 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} y = 15 - 3x &\\ 2x - 5y = 0 & \end{cases} \end{equation*}$
2x − 5(15 − 3x) = 0
2x − 75 + 15x = 0
17x = 75
$x = \frac{75}{17} = 4\frac{7}{17}$
$y = 15 - 3 * \frac{75}{17} = 15 - \frac{225}{17} = 15 - 13\frac{4}{17} = 1\frac{13}{17}$
Ответ: $x = 4\frac{7}{17}, y = 1\frac{13}{17}$.

$\begin{equation*} \begin{cases} 3m + 5n = 1 &\\ \frac{m}{4} + \frac{3n}{5} = 1 |*20 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 3m + 5n = 1 |*5 &\\ 5m + 12n = 20 |*3 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 15m + 25n = 5 &\\ 15m + 36n = 60 & \end{cases} \end{equation*}$
15m + 25n − (15m + 36n) = 5 − 60
15m + 25n − 15m − 36n = −55
−11n = −55
n = 5
3m + 5 * 5 = 1
3m + 25 = 1
3m = 1 − 25
3m = −24
m = −8
Ответ: m = −8; n = 5.

$\begin{equation*} \begin{cases} 4x - 3y = 1 &\\ \frac{2x + 1}{6} = \frac{9 - 5y}{8} |*24 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 4x - 3y = 1 &\\ 4(2x + 1) = 3(9 - 5y) & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 4x - 3y = 1 &\\ 8x + 4 = 27 - 15y & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 4x - 3y = 1 |*5 &\\ 8x + 15y = 27 - 4 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 20x - 15y = 5 &\\ 8x + 15y = 23 & \end{cases} \end{equation*}$
20x − 15y + 8x + 15y = 5 + 23
28x = 28
x = 1
4 * 1 − 3y = 1
−3y = 1 − 4
−3y = −3
y = 1
Ответ: x = 1, y = 1.

$\begin{equation*} \begin{cases} 3q = 4p - 7 &\\ \frac{1 - 3q}{4} = \frac{4 - 2p}{3} |*12 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 3q = 4p - 7 &\\ 3(1 - 3q) = 4(4 - 2p) & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 3q - 4p = -7 &\\ 3 - 9q = 16 - 8p & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 3q - 4p = -7 |*2 &\\ -9q + 8p = 16 - 3 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 6q - 8p = -14 &\\ -9q + 8p = 13 & \end{cases} \end{equation*}$
6q − 8p − 9q + 8p = −14 + 13
−3q = −1
$q = \frac{1}{3}$
$3 * \frac{1}{3} = 4p - 7$
1 = 4p − 7
4p = 1 + 7
4p = 8
p = 2
Ответ: p = 2, $q = \frac{1}{3}$.