$\begin{equation*} \begin{cases} \frac{3x - 2}{4y + 3} = \frac{4}{15} &\\ \frac{5x - y}{3y - 2} = 1 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 15(3x - 2) = 4(4y + 3) &\\ 5x - y = 3y - 2 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 45x - 30 = 16y + 12 &\\ 5x - y = 3y - 2 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 45x - 16y = 30 + 12 &\\ 5x - y - 3y = -2 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 45x - 16y = 42 &\\ 5x - 4y = -2 | * (-4) & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 45x - 16y = 42 &\\ -20x + 16y = 8 & \end{cases} \end{equation*}$
45x − 16y − 20x + 16y = 42 + 8
25x = 50
x = 50 : 25
x = 2
5x − 4y = −2
4y = 5x + 2
4y = 5 * 2 + 2
4y = 10 + 2
4y = 12
y = 12 : 4
y = 3
Ответ: (2;3)