$\begin{equation*} \begin{cases} 5x - 3y = 14 &\\ 2x + y = 10 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 5x - 3y = 14 &\\ y = 10 - 2x & \end{cases} \end{equation*}$
5x − 3 * (10 − 2x) = 14
5x − 30 + 6x = 14
11x = 14 + 30
11x = 44
x = 44 : 11
x = 4
y = 10 − 2x = 10 − 2 * 4 = 10 − 8 = 2
Ответ: (4;2)

$\begin{equation*} \begin{cases} x + 5y = 35 &\\ 3x + 2y = 27 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} x = 35 - 5y &\\ 3x + 2y = 27 & \end{cases} \end{equation*}$
3 * (35 − 5y) + 2y = 27
105 − 15y + 2y = 27
−13y = 27 − 105
−13y = −78
y = −78 : (−13)
y = 6
x = 35 − 5y = 35 − 5 * 6 = 35 − 30 = 5
Ответ: (5;6)

$\begin{equation*} \begin{cases} 7x - 2y = 15 &\\ 2x + y = 9 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 7x - 2y = 15 &\\ y = 9 - 2x & \end{cases} \end{equation*}$
7x − 2 * (9 − 2x) = 15
7x − 18 + 4x = 15
11x = 15 + 18
11x = 33
x = 33 : 11
x = 3
y = 9 − 2x = 9 − 2 * 3 = 9 − 6 = 3
Ответ: (3;3)

$\begin{equation*} \begin{cases} x + 3y = 2 &\\ 2x + 3y = 7 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} x = 2 - 3y &\\ 2x + 3y = 7 & \end{cases} \end{equation*}$
2 * (2 − 3y) + 3y = 7
4 − 6y + 3y = 7
−3y = 7 − 4
−3y = 3
y = 3 : (−3)
y = −1
x = 2 − 3y = 2 − 3 * (−1) = 2 + 3 = 5
Ответ: (5;−1)