$\begin{equation*} \begin{cases} 3x + 4y = 0 &\\ 2x + 3y = 1 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 3x + 4y = 0 &\\ 2x = 1 - 3y & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 3x + 4y = 0 &\\ x = 0,5 - 1,5y & \end{cases} \end{equation*}$
3(0,5 − 1,5y) + 4y = 0
1,5 − 4,5y + 4y = 0
−0,5y = −1,5
y = 3
x = 0,5 − 1,5 * 3 = 0,5 − 4,5 = −4
Ответ: x = −4, y = 3.

$\begin{equation*} \begin{cases} 7x + 2y = 0 &\\ 4y + 9x = 10 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 2y = -7x &\\ 4y + 9x = 10 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} y = -3,5x &\\ 4y + 9x = 10 & \end{cases} \end{equation*}$
4 * (−3,5x) + 9x = 10
−14x + 9x = 10
−5x = 10
x = −2
y = −3,5 * (−2) = 7
Ответ: x = −2, y = 7.

$\begin{equation*} \begin{cases} 5x + 6y = -20 &\\ 9y + 2x = 25 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 5x + 6y = -20 &\\ 2x = 25 - 9y & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 5x + 6y = -20 &\\ x = 12,5 - 4,5y & \end{cases} \end{equation*}$
5(12,5 − 4,5y) + 6y = −20
62,5 − 22,5y + 6y = −20
−16,5y = −20 − 62,5
−16,5y = −82,5
y = 5
x = 12,5 − 4,5 * 5 = 12,5 − 22,5 = −10
Ответ: x = −10, y = 5.

$\begin{equation*} \begin{cases} 3x + 1 = 8y &\\ 11y - 3x = -11 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 3x = 8y - 1 &\\ 11y - 3x = -11 & \end{cases} \end{equation*}$
11y − (8y − 1) = −11
11y − 8y + 1 = −11
3y = −11 − 1
3y = −12
y = −4
3x = 8 * (−4) − 1
3x = −32 − 1
3x = −33
x = −11
Ответ: x = −11, y = −4.