$\begin{equation*} \begin{cases} 2u + 5v = 0 &\\ -8u + 15v = 7 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 2u = -5v &\\ -8u + 15v = 7 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} u = -2,5v &\\ -8u + 15v = 7 & \end{cases} \end{equation*}$
−8 * (−2,5v) + 15v = 7
20v + 15v = 7
35v = 7
v = 0,2
u = −2,5 * 0,2 = −0,5
Ответ: v = 0,2, u = −0,5.

$\begin{equation*} \begin{cases} 5p - 3q = 0 &\\ 3p + 4q = 29 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 5p = 3q &\\ 3p + 4q = 29 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} p = 0,6q &\\ 3p + 4q = 29 & \end{cases} \end{equation*}$
3 * 0,6q + 4q = 29
1,8q + 4q = 29
5,8q = 29
q = 5
p = 0,6 * 5 = 3
Ответ: q = 5, p = 3.

$\begin{equation*} \begin{cases} 4u + 3v = 14 &\\ 5u - 3v = 25 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 3v = 14 - 4u &\\ 5u - 3v = 25 & \end{cases} \end{equation*}$
5u − (14 − 4u) = 25
5u − 14 + 4u = 25
9u = 25 + 14
9u = 39
$u = \frac{39}{9} = \frac{13}{3} = 4\frac{1}{3}$
$3v = 14 - 4 * \frac{13}{3}$
$3v = 14 - \frac{52}{3}$
$3v = 14 - 17\frac{1}{3}$
$3v = -3\frac{1}{3}$
$v = -\frac{10}{3} : 3$
$v = -\frac{10}{3} * \frac{1}{3}$
$v = -\frac{10}{9} = -1\frac{1}{9}$
Ответ: $v = -1\frac{1}{9}, u = 4\frac{1}{3}$.

$\begin{equation*} \begin{cases} 10p + 7q = -2 &\\ 2p - 22 = 5q & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 10p + 7q = -2 &\\ 2p = 5q + 22 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 10p + 7q = -2 &\\ p = 2,5q + 11 & \end{cases} \end{equation*}$
10(2,5q + 11) + 7q = −2
25q + 110 + 7q = −2
32q = −2 − 110
32q = −112
q = −3,5
p = 2,5 * (−3,5) + 11 = −8,75 + 11 = 2,25
Ответ: q = −3,5, p = 2,25.