$\begin{equation*} \begin{cases} \frac{x}{3} + \frac{y}{4} - 5 = 0 |*12 &\\ 2x - y = 10 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 4x + 3y - 60 = 0 &\\ 2x - y = 10 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 4x + 3y = 60 &\\ 2x - y = 10 |*2 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 4x + 3y = 60 &\\ 4x - 2y = 20 & \end{cases} \end{equation*}$
4x + 3y − (4x − 2y) = 60 − 20
4x + 3y − 4x + 2y = 40
5y = 40
y = 8
2x − 8 = 10
2x = 10 + 8
2x = 18
x = 9
Ответ: x = 9, y = 8.

$\begin{equation*} \begin{cases} 2x - 7y = 4 &\\ \frac{x}{6} - \frac{y}{6} = 0 |*6 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 2x - 7y = 4 &\\ x - y = 0 |*2 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 2x - 7y = 4 &\\ 2x - 2y = 0 & \end{cases} \end{equation*}$
2x − 7y − (2x − 2y) = 4 − 0
2x − 7y − 2x + 2y = 4
−5y = 4
y = −0,8
x − (−0,8) = 0
x + 0,8 = 0
x = −0,8
Ответ: x = −0,8, y = −0,8.

$\begin{equation*} \begin{cases} \frac{2x}{3} - \frac{y}{2} = 0 |*6 &\\ 3(x - 1) - 9 = 1 - y & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 4x - 3y = 0 &\\ 3x - 3 - 9 = 1 - y & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 4x - 3y = 0 &\\ 3x + y = 1 + 12 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 4x - 3y = 0 &\\ 3x + y = 13 |*3 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 4x - 3y = 0 &\\ 9x + 3y = 39 & \end{cases} \end{equation*}$
4x − 3y + 9x + 3y = 0 + 39
13x = 39
x = 3
3 * 3 + y = 13
y = 13 − 9
y = 4
Ответ: x = 3, y = 4.

$\begin{equation*} \begin{cases} \frac{5x}{6} - y = -\frac{5}{6} |*6 &\\ \frac{2x}{3} + 3y = -\frac{2}{3} |*3 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 5x - 6y = -5 |*2 &\\ 2x + 9y = -2 |*5 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 10x - 12y = -10 &\\ 10x + 45y = -10 & \end{cases} \end{equation*}$
10x − 12y − (10x + 45y) = −10 − (−10)
10x − 12y − 10x − 45y = −10 + 10
−57y = 0
y = 0
2x + 9 * 0 = −2
2x = −2
x = −1
Ответ: x = −1, y = 0.