\begin{equation*} \begin{cases} 3x + 7y = 1 | * 5 &\\ 6y - 5x = 16 | * 3 & \end{cases} \end{equation*}
\begin{equation*} \begin{cases} 15x + 35y = 5 &\\ 18y - 15x = 48 & \end{cases} \end{equation*}
15x + 35y + 18y − 15x = 5 + 48
53y = 53
y = 53 : 53
y = 1;
3x + 7 * 1 = 1
3x = 1 − 7
x = −6 : 3
x = −2.
Ответ: (−2;1).

\begin{equation*} \begin{cases} 3x - 5y = 19 | * -2 &\\ 2x + 3y = 0 | * 3& \end{cases} \end{equation*}
\begin{equation*} \begin{cases} -6x + 10y = -38 &\\ 6x + 9y = 0 & \end{cases} \end{equation*}
−6x + 10y + 6x + 9y = −38
10y + 9y = −38
y = −38 : 19
y = −2;
2x + 3 * −2 = 0
2x = 6
x = 6 : 2
x = 3.
Ответ: (3;−2).

\begin{equation*} \begin{cases} 3(2a - 1) + 6(7 - b) = 51 &\\ 2(a + 6) - 7(1 + 6b) = 49 & \end{cases} \end{equation*}
\begin{equation*} \begin{cases} 6a - 3 + 42 - 6b = 51 &\\ 2a + 12 - 7 - 42b = 49 & \end{cases} \end{equation*}
\begin{equation*} \begin{cases} 6a - 6b = 51 + 3 - 42 &\\ 2a - 42b = 49 - 12 + 7 & \end{cases} \end{equation*}
\begin{equation*} \begin{cases} 6a - 6b = 12 | : 6 &\\ 2a - 42b = 44 | * -2 & \end{cases} \end{equation*}
\begin{equation*} \begin{cases} a - b = 2 | : 6 &\\ -a + 21b = -22 | * -2 & \end{cases} \end{equation*}
a − b − a + 21b = 2 − 22
20b = −20
b = −20 : 20
b = −1;
a − b = 2
a + 1 = 2
a = 2 − 1 = 1.
Ответ: (1;−1).

\begin{equation*} \begin{cases} \frac{3x - 2y}{4} - \frac{4x + 5}{3} = -5 | * 12 &\\ \frac{6x - 5y}{2} + \frac{2x + y}{5} = 9 | * 10 & \end{cases} \end{equation*}
\begin{equation*} \begin{cases} 3(3x - 2y) - 4(4x + 5) = -60 &\\ 5(6x - 5y) + 2(2x + y) = 90& \end{cases} \end{equation*}
\begin{equation*} \begin{cases} 9x - 6y - 16x - 20 = -60 &\\ 30x - 25y + 4x + 2y = 90& \end{cases} \end{equation*}
\begin{equation*} \begin{cases} -7x - 6y = -60 + 20 &\\ 34x - 23y = 90& \end{cases} \end{equation*}
\begin{equation*} \begin{cases} -7x - 6y = -40 | * -23 &\\ 34x - 23y = 90 | * 6 & \end{cases} \end{equation*}
\begin{equation*} \begin{cases} 161x + 138y = 920 &\\ 204x - 138y = 540 & \end{cases} \end{equation*}
161x + 138y + 204x − 138y = 920 + 540
365x = 1460
x = 1460 : 365
x = 4;
−7 * 4 − 6y = −40
−6y = −40 + 28
−6y = −12
y = −12 : −6
y = 2.
Ответ: (4;2).