$\begin{equation*} \begin{cases} 6y - 5x - 1 = 0 &\\ \frac{x - 1}{3} + \frac{y + 1}{2} = 10 | *6 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 6y - 5x = 1 &\\ 2(x - 1) + 3(y + 1) = 60 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 6y - 5x = 1 &\\ 2x - 2 + 3y + 3 = 60 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 6y - 5x = 1 &\\ 2x + 3y = 60 + 2 - 3 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 6y - 5x = 1 &\\ 2x + 3y = 59 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 6y - 5x = 1 &\\ 2x = 59 - 3y & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 6y - 5x = 1 &\\ x = 29,5 - 1,5y & \end{cases} \end{equation*}$
6y − 5x = 1
6y − 5 * (29,5 − 1,5y) = 1
6y − 147,5 + 7,5y = 1
13,5y = 1 + 147,5
y = 148,5 : 13,5
y = 11
x = 29,5 − 1,5y = 29,5 − 1,5 * 11 = 29,5 − 16,5 = 13
Ответ: (13;11)

$\begin{equation*} \begin{cases} \frac{x + 2y}{5} + \frac{3x - y}{3} = 5 | *15 &\\ 2x - 3y = -1 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 3(x + 2y) + 5(3x - y) = 75 &\\ 2x - 3y = -1 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 3x + 6y + 15x - 5y = 75 &\\ 2x - 3y = -1 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 18x + y = 75 &\\ 2x - 3y = -1 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} y = 75 - 18x &\\ 2x - 3y = -1 & \end{cases} \end{equation*}$
2x − 3y = −1
2x − 3(75 − 18x) = −1
2x − 225 + 54x = −1
56x = −1 + 225
56x = 224
x = 224 : 56
x = 4
y = 75 − 18x = 75 − 18 * 4 = 75 − 72 = 3
Ответ: (4;3)

$\begin{equation*} \begin{cases} \frac{3x + 2y}{5} + \frac{x - 3y}{6} = 3 | *30 &\\ 2x + 7y + 43 = 0 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 6(3x + 2y) + 5(x - 3y) = 90 &\\ 2x + 7y = -43 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 18x + 12y + 5x - 15y = 90 &\\ 2x + 7y = -43 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 23x - 3y = 90 &\\ 2x = -43 - 7y & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 23x - 3y = 90 &\\ x = -21,5 - 3,5y & \end{cases} \end{equation*}$
23(−21,5 − 3,5y) − 3y = 90
−494,5 − 80,5y − 3y = 90
−83,5y = 90 + 494,5
y = 584,5 : (−83,5)
y = −7
x = −21,5 − 3,5y = −21,5 − 3,5 * (−7) = −21,5 + 24,5 = 3
Ответ: (3;−7)

$\begin{equation*} \begin{cases} 7x - 10y = 5 &\\ \frac{4x + 1}{3} - \frac{5x - 3y}{4} = 3 | *12 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 7x - 10y = 5 &\\ 4(4x + 1) - 3(5x - 3y) = 36 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 7x - 10y = 5 &\\ 16x + 4 - 15x + 9y = 36 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 7x - 10y = 5 &\\ x + 9y = 36 - 4 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 7x - 10y = 5 &\\ x = 32 - 9y & \end{cases} \end{equation*}$
7x − 10y = 5
7(32 − 9y) − 10y = 5
224 − 63y − 10y = 5
−73y = 5 − 224
y = −219 : (−73)
y = 3
x = 32 − 9y = 32 − 9 * 3 = 32 − 27 = 5
Ответ: (5;3)