$\begin{equation*} \begin{cases} 40x + 3y = 10 &\\ 20x - 7y = 5 |*2 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 40x + 3y = 10 &\\ 40x - 14y = 10 & \end{cases} \end{equation*}$
40x + 3y − (40x − 14y) = 10 − 10
40x + 3y − 40x + 14y = 0
17y = 0
y = 0
40x + 3 * 0 = 10
40x = 10
x = 0,25
Ответ: x = 0,25, y = 0.

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

$\begin{equation*} \begin{cases} 33a + 42b = 10 &\\ 9a + 14b = 4 |*3 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 33a + 42b = 10 &\\ 27a + 42b = 12 & \end{cases} \end{equation*}$
33a + 42b − (27a + 42b) = 10 − 12
33a + 42b − 27a − 42b = −2
6a = −2
$a = -\frac{1}{3}$
$9 * (-\frac{1}{3}) + 14b = 4$
−3 + 14b = 4
14b = 4 + 3
14b = 7
$b = \frac{1}{2}$
Ответ: $a = -\frac{1}{3}, b = \frac{1}{2}.$

$\begin{equation*} \begin{cases} 13x - 12y = 14 &\\ 11x - 4 = 18y & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 13x - 12y = 14 |*3 &\\ 11x - 18y = 4 |*2 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 39x - 36y = 42 &\\ 22x - 36y = 8 & \end{cases} \end{equation*}$
39x − 36y − (22x − 36y) = 42 − 8
39x − 36y − 22x + 36y = 34
17x = 34
x = 2
13 * 2 − 12y = 14
26 − 12y = 14
−12y = 14 − 26
−12y = −12
y = 1
Ответ: x = 2, y = 1.

$\begin{equation*} \begin{cases} 10x - 9y = 8 |*3 &\\ 21y + 15x = 0,5 |*2 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 30x - 27y = 24 &\\ 42y + 30x = 1 & \end{cases} \end{equation*}$
30x − 27y − (42y + 30x) = 24 − 1
30x − 27y − 42y − 30x = 23
−69y = 23
$y = -\frac{1}{3}$
$10x - 9 * (-\frac{1}{3}) = 8$
10x + 3 = 8
10x = 8 − 3
10x = 5
$x = \frac{1}{2}$
Ответ: $x = \frac{1}{2}, y = -\frac{1}{3}.$

$\begin{equation*} \begin{cases} 9y + 8z = -2 &\\ 5z = -4y - 11 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 9y + 8z = -2 |*5 &\\ 5z + 4y = -11 |*8 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 45y + 40z = -10 &\\ 40z + 32y = -88 & \end{cases} \end{equation*}$
45y + 40z − (40z + 32y) = −10 − (−88)
45y + 40z − 40z − 32y = −10 + 88
13y = 78
y = 6
9 * 6 + 8z = −2
8z = −2 − 54
8z = −56
z = −7
Ответ: y = 6, z = −7.