3x − 2y = 8
2y = 3x − 8
y = 1,5x − 4
$\begin{equation*} \begin{cases} y = 1,5x - 4 &\\ y = x & \end{cases} \end{equation*}$
x = 1,5x − 4
x − 1,5x = −4
−0,5x = −4
x = −4 : (−0,5)
x = 8
y = x = 8
Ответ: (8;8)

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

−3x − 7y = 2
−7y = 3x + 2
7y = −3x − 2
$y = -\frac{3}{7}x - \frac{2}{7}$
$\begin{equation*} \begin{cases} y = -\frac{3}{7}x - \frac{2}{7} &\\ y = x & \end{cases} \end{equation*}$
$x = -\frac{3}{7}x - \frac{2}{7}$
$x + \frac{3}{7}x = -\frac{2}{7}$
$\frac{10}{7}x = -\frac{2}{7}$
$x = -\frac{2}{7} : \frac{10}{7}$
$x = -\frac{2}{7} * \frac{7}{10}$
$x = -\frac{2}{10} = -0,2$
y = x = −0,2
Ответ: (−0,2;−0,2)

5x + 6y = 9
6y = −5x + 9
$y = -\frac{5}{6}x + \frac{9}{6}$
$y = -\frac{5}{6}x + \frac{3}{2}$
$\begin{equation*} \begin{cases} y = -\frac{5}{6}x + \frac{3}{2} &\\ y = x & \end{cases} \end{equation*}$
$x = -\frac{5}{6}x + \frac{3}{2}$
$x + \frac{5}{6}x = \frac{3}{2}$
$\frac{11}{6}x = \frac{3}{2}$
$x = \frac{3}{2} : \frac{11}{6}$
$x = \frac{3}{2} * \frac{6}{11}$
$x = \frac{9}{11}$
$y = x = \frac{9}{11}$
Ответ: $(\frac{9}{11};\frac{9}{11})$