$\begin{equation*} \begin{cases} (x - 1)^2 - (x + 2)^2 = 9y &\\ (y - 3)^2 - (y + 2)^2 = 5x & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} x^2 - 2x + 1 - (x^2 + 4x + 4) = 9y &\\ y^2 - 6y + 9 - (y^2 + 4y + 4) = 5x & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} x^2 - 2x + 1 - x^2 - 4x - 4 = 9y &\\ y^2 - 6y + 9 - y^2 - 4y - 4 = 5x & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} x^2 - 2x - x^2 - 4x - 9y = 4 - 1 &\\ y^2 - 6y - y^2 - 4y - 5x = 4 - 9 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} -6x - 9y = 3 |*5 &\\ -10y - 5x = -5 |*6 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} -30x - 45y = 15 &\\ -60y - 30x = -30 & \end{cases} \end{equation*}$
−30x − 45y − (−60y − 30x) = 15 − (−30)
−30x − 45y + 60y + 30x = 15 + 30
15y = 45
y = 3
−6x − 9y = 3
−6x − 9 * 3 = 3
−6x − 27 = 3
−6x = 3 + 27
−6x = 30
x = −5
Ответ: x = −5, y = 3.

$\begin{equation*} \begin{cases} (7 + u)^2 - (5 + u)^2 = 6v &\\ (2 - v)^2 - (6 - v)^2 = 4u & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 49 + 14u + u^2 - (25 + 10u + u^2) = 6v &\\ 4 - 4v + v^2 - (36 - 12v + v^2) = 4u & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 49 + 14u + u^2 - 25 - 10u - u^2 = 6v &\\ 4 - 4v + v^2 - 36 + 12v - v^2 = 4u & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 14u + u^2 - 10u - u^2 - 6v = -49 + 25 &\\ -4v + v^2 + 12v - v^2 - 4u = -4 + 36 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 4u - 6v = -24 &\\ 8v - 4u = 32 & \end{cases} \end{equation*}$
4u − 6v + 8v − 4u = −24 + 32
2v = 8
v = 4
4u − 6 * 4 = −24
4u − 24 = −24
4u = −24 + 24
4u = 0
u = 0
Ответ: v = 4, u = 0.