$\begin{equation*} \begin{cases} 6(x + y) = 8 + 2x - 3y &\\ 5(y - x) = 5 + 3x + 2y & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 6x + 6y - 2x + 3y = 8 &\\ 5y - 5x - 3x - 2y = 5 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 4x + 9y = 8 &\\ 3y - 8x = 5 |*3 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 4x + 9y = 8 &\\ 9y - 24x = 15 & \end{cases} \end{equation*}$
4x + 9y − (9y − 24x) = 8 − 15
4x + 9y − 9y + 24x = −7
28x = −7
x = −0,25
4 * (−0,25) + 9y = 8
−1 + 9y = 8
9y = 8 + 1
9y = 9
y = 1
Ответ: x = −0,25, y = 1.

$\begin{equation*} \begin{cases} -2(2x + 1) + 1,5 = 3(y - 2) - 6x &\\ 11,5 - 4(3 - x) = 2y - (5 - x) & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} -4x - 2 + 1,5 = 3y - 6 - 6x &\\ 11,5 - 12 + 4x = 2y - 5 + x & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} -4x + 6x - 3y = -6 + 2 - 1,5 &\\ 4x - 2y - x = -5 - 11,5 + 12 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 2x - 3y = -5,5 |*3 &\\ 3x - 2y = -4,5 |*2 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 6x - 9y = -16,5 &\\ 6x - 4y = -9 & \end{cases} \end{equation*}$
6x − 9y − (6x − 4y) = −16,5 − (−9)
6x − 9y − 6x + 4y = −16,5 + 9
−5y = −7,5
y = 1,5
3x − 2 * 1,5 = −4,5
3x − 3 = −4,5
3x = −4,5 + 3
3x = −1,5
x = −0,5
Ответ: x = −0,5, y = 1,5.

$\begin{equation*} \begin{cases} 4(2x - y + 3) - 3(x - 2y + 3) = 48 &\\ 3(3x - 4y + 3) + 4(4x - 2y - 9) = 48 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 8x - 4y + 12 - 3x + 6y - 9 = 48 &\\ 9x - 12y + 9 + 16x - 8y - 36 = 48 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 5x + 2y = 48 - 12 + 9 &\\ 25x - 20y = 48 - 9 + 36 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 5x + 2y = 45 &\\ 25x - 20y = 75 |:5 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 5x + 2y = 45 &\\ 5x - 4y = 15 & \end{cases} \end{equation*}$
5x + 2y − (5x − 4y) = 45 − 15
5x + 2y − 5x + 4y = 30
6y = 30
y = 5
5x + 2 * 5 = 45
5x + 10 = 45
5x = 45 − 10
5x = 35
x = 7
Ответ: x = 7, y = 5.

$\begin{equation*} \begin{cases} 84 + 3(x - 3y) = 36x - 4(y + 17) &\\ 10(x - y) = 3y + 4(1 - x) & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 84 + 3x - 9y = 36x - 4y - 68 &\\ 10x - 10y = 3y + 4 - 4x & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 3x - 36x - 9y + 4y = -68 - 84 &\\ 10x + 4x - 10y - 3y = 4 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} -33x - 5y = -152 |*13 &\\ 14x - 13y = 4 |*5 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} -429x - 65y = -1976 &\\ 70x - 65y = 20 & \end{cases} \end{equation*}$
−429x − 65y − (70x − 65y) = −1976 − 20
−499x = −1996
x = 4
14 * 4 − 13y = 4
56 − 13y = 4
−13y = 4 − 56
−13y = −52
y = 4
Ответ: x = 4, y = 4.