$\begin{equation*} \begin{cases} 5x + 3y = -12 &\\ -2x + 4y = 10 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 5x + 3y = -12 &\\ -2x = 10 - 4y & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 5x + 3y = -12 &\\ x = 2y - 5 & \end{cases} \end{equation*}$
5(2y − 5) + 3y = −12
10y − 25 + 3y = −12
13y = −12 + 25
13y = 13
y = 1
x = 2y − 5
x = 2 * 1 − 5
x = 2 − 5
x = −3
Ответ: (−3; 1)

$\begin{equation*} \begin{cases} 9x + 8y = 21 &\\ 6x + 4y = 13 |* (-2) & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 9x + 8y = 21 &\\ -12x - 8y = -26 & \end{cases} \end{equation*}$
9x + 8y − 12x − 8y = 21 − 26
−3x = −5
$x = \frac{5}{3} = 1\frac{2}{3}$
$9 * \frac{5}{3} + 8y = 21$
3 * 5 + 8y = 21
15 + 8y = 21
8y = 21 − 15
8y = 6
$y = \frac{6}{8} = \frac{3}{4}$
Ответ: $(1\frac{2}{3}; \frac{3}{4})$

$\begin{equation*} \begin{cases} -6x - 7y = 8 |* 2 &\\ 4x + 3y = -2 | * 3 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} -12x - 14y = 16 &\\ 12x + 9y = -6 & \end{cases} \end{equation*}$
−12x − 14y + 12x + 9y = 16 − 6
−5y = 10
y = −2
4x + 3y = −2
4x + 3 * (−2) = −2
4x − 6 = −2
4x = −2 + 6
4x = 4
x = 1
Ответ: (1; −2)

$\begin{equation*} \begin{cases} 3y - 4x = -6 |* 3 &\\ 5x - 9y = -10 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 9y - 12x = -18 &\\ 5x - 9y = -10 & \end{cases} \end{equation*}$
9y − 12x + 5x − 9y = −18 − 10
−7x = −28
x = 4
3y − 4x = −6
3y − 4 * 4 = −6
3y − 16 = −6
3y = −6 + 16
3y = 10
$y = \frac{10}{3} = 3\frac{1}{3}$
Ответ: $(4; 3\frac{1}{3})$