$\begin{equation*} \begin{cases} 4x - 3y = 12 &\\ 3x + 4y = -24 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 4x = 12 + 3y &\\ 3x + 4y = -24 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} x = 3 + 0,75y &\\ 3x + 4y = -24 & \end{cases} \end{equation*}$
3x + 4y = −24
3 * (3 + 0,75y) + 4y = −24
9 + 2,25y + 4y = −24
6,25y = −24 − 9
6,25y = −33
y = −33 : 6,25
y = −5,28
x = 3 + 0,75y = 3 + 0,75 * (−5,28) = 3 − 3,96 = −0,96
Ответ: −0,96

$\begin{equation*} \begin{cases} 5x + 2y = 20 &\\ 2x - 5y = 10 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 2y = 20 - 5x &\\ 2x - 5y = 10 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} y = 10 - 2,5x &\\ 2x - 5y = 10 & \end{cases} \end{equation*}$
2x − 5 * (10 − 2,5x) = 10
2x − 50 + 12,5x = 10
14,5x = 10 + 50
14,5x = 60
$x = \frac{60}{14,5} = \frac{600}{145} = \frac{120}{29} = 4\frac{4}{29}$
Ответ: $4\frac{4}{29}$

$\begin{equation*} \begin{cases} 2x - 3y = 12 &\\ 3x + 2y = 6 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 2x - 3y = 12 &\\ 2y = 6 - 3x & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 2x - 3y = 12 &\\ y = 3 - 1,5x & \end{cases} \end{equation*}$
2x − 3y = 12
2x − 3(3 − 1,5x) = 12
2x − 9 + 4,5x = 12
6,5x = 12 + 9
6,5x = 21
x = 21 : 6,5
$x = \frac{21}{6,5} = \frac{210}{65} = \frac{42}{13} = 3\frac{3}{13}$
Ответ: $3\frac{3}{13}$

$\begin{equation*} \begin{cases} 5x - 3y = 5 &\\ 2x + 7y = 4 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 3y = 5x - 5 &\\ 2x + 7y = 4 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} y = \frac{5}{3}x - \frac{5}{3} &\\ 2x + 7y = 4 & \end{cases} \end{equation*}$
2x + 7y = 4
$2x + 7 * (\frac{5}{3}x - \frac{5}{3}) = 4$
$2x + \frac{35}{3}x - \frac{35}{3} = 4$
$\frac{41}{3}x = 4 + \frac{35}{3}$
$\frac{41}{3}x = \frac{47}{3}$
$x = \frac{47}{3} : \frac{41}{3}$
$x = \frac{47}{3} * \frac{3}{41}$
$x = \frac{47}{41} = 1\frac{6}{41}$
Ответ: $1\frac{6}{41}$