Решите систему уравнений:
а)
$\begin{equation*}
\begin{cases}
5y + 8(x - 3y) = 7x - 12 &\\
9x + 3(x - 9y) = 11y + 46 &
\end{cases}
\end{equation*}$
б)
$\begin{equation*}
\begin{cases}
-2(a - b) + 16 = 3(b + 7) &\\
6a - (a - 5) = -8 - (b + 1) &
\end{cases}
\end{equation*}$
$\begin{equation*}
\begin{cases}
5y + 8(x - 3y) = 7x - 12 &\\
9x + 3(x - 9y) = 11y + 46 &
\end{cases}
\end{equation*}$
$\begin{equation*}
\begin{cases}
5y + 8x - 24y = 7x - 12 &\\
9x + 3x - 27y = 11y + 46 &
\end{cases}
\end{equation*}$
$\begin{equation*}
\begin{cases}
8x - 7x - 19y = -12 &\\
12x - 27y - 11y = 46 &
\end{cases}
\end{equation*}$
$\begin{equation*}
\begin{cases}
x = 19y - 12 &\\
12x - 38y = 46 &
\end{cases}
\end{equation*}$
12(19y − 12) − 38y = 46
228y − 144 − 38y = 46
190y = 46 + 144
190y = 190
y = 1
x = 19 * 1 − 12 = 7
Ответ: x = 7, y = 1.
$\begin{equation*}
\begin{cases}
-2(a - b) + 16 = 3(b + 7) &\\
6a - (a - 5) = -8 - (b + 1) &
\end{cases}
\end{equation*}$
$\begin{equation*}
\begin{cases}
-2a + 2b + 16 = 3b + 21 &\\
6a - a + 5 = -8 - b - 1 &
\end{cases}
\end{equation*}$
$\begin{equation*}
\begin{cases}
-2a + 2b - 3b = 21 - 16 &\\
5a + b = -9 - 5 &
\end{cases}
\end{equation*}$
$\begin{equation*}
\begin{cases}
-2a - b = 5 &\\
5a + b = -14 &
\end{cases}
\end{equation*}$
$\begin{equation*}
\begin{cases}
b = -2a - 5 &\\
5a + b = -14 &
\end{cases}
\end{equation*}$
5a − 2a − 5 = −14
3a = −14 + 5
3a = −9
a = −3
b = −2 * (−3) − 5 = 6 − 5 = 1
Ответ: a = −3, b = 1.
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