Решите систему уравнений:
а)
$\begin{equation*}
\begin{cases}
2x + 11y = 15 &\\
10x - 11y = 9 &
\end{cases}
\end{equation*}$
б)
$\begin{equation*}
\begin{cases}
8x - 17y = 4 &\\
-8x + 15y = 4 &
\end{cases}
\end{equation*}$
в)
$\begin{equation*}
\begin{cases}
4x - 7y = 30 &\\
4x - 5y = 90 &
\end{cases}
\end{equation*}$
г)
$\begin{equation*}
\begin{cases}
13x - 8y = 28 &\\
11x - 8y = 24 &
\end{cases}
\end{equation*}$
$\begin{equation*}
\begin{cases}
2x + 11y = 15 &\\
10x - 11y = 9 &
\end{cases}
\end{equation*}$
2x + 11y + 10x − 11y = 15 + 9
12x = 24
x = 2
2 * 2 + 11y = 15
11y = 15 − 4
11y = 11
y = 1
Ответ: x = 2, y = 1.
$\begin{equation*}
\begin{cases}
8x - 17y = 4 &\\
-8x + 15y = 4 &
\end{cases}
\end{equation*}$
8x − 17y − 8x + 15y = 4 + 4
−2y = 8
y = −4
8x − 17 * (−4) = 4
8x + 68 = 4
8x = 4 − 68
8x = −64
x = −8
Ответ: x = −8, y = −4.
$\begin{equation*}
\begin{cases}
4x - 7y = 30 &\\
4x - 5y = 90 &
\end{cases}
\end{equation*}$
4x − 7y − (4x − 5y) = 30 − 90
4x − 7y − 4x + 5y = −60
−2y = −60
y = 30
4x − 7 * 30 = 30
4x − 210 = 30
4x = 30 + 210
4x = 240
x = 60
Ответ: x = 60, y = 30.
$\begin{equation*}
\begin{cases}
13x - 8y = 28 &\\
11x - 8y = 24 &
\end{cases}
\end{equation*}$
13x − 8y − (11x − 8y) = 28 − 24
13x − 8y − 11x + 8y = 4
2x = 4
x = 2
11 * 2 − 8y = 24
8y = 22 − 24
8y = −2
y = −0,25
Ответ: x = 2, y = −0,25.
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