Đáp án:
c. \(\left\{ \begin{array}{l}
y = - 4\\
x = - 3\\
z = - 5
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
a.\left\{ \begin{array}{l}
8x = 9y\\
3x - 2y = 11
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = \dfrac{9}{8}y\\
3.\dfrac{9}{8}y - 2y = 11
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = \dfrac{9}{8}y\\
\dfrac{{11}}{8}y = 11
\end{array} \right.\\
\to \left\{ \begin{array}{l}
y = 8\\
x = 9
\end{array} \right.\\
b.\left\{ \begin{array}{l}
x = \dfrac{3}{{10}}y:\dfrac{2}{5}\\
z = \dfrac{3}{{10}}y:\dfrac{1}{{12}}\\
x + y + z = 109
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = \dfrac{3}{4}y\\
z = \dfrac{{18}}{5}y\\
\dfrac{3}{4}y + y + \dfrac{{18}}{5}y = 109
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = \dfrac{3}{4}y\\
z = \dfrac{{18}}{5}y\\
\dfrac{{107}}{{20}}y = 109
\end{array} \right.\\
\to \left\{ \begin{array}{l}
y = \dfrac{{2180}}{{107}}\\
x = \dfrac{{1635}}{{107}}\\
z = \dfrac{{7848}}{{107}}
\end{array} \right.\\
c.\left\{ \begin{array}{l}
3x - 3 = 2y - 4\\
4y - 8 = 3z - 9\\
x - 2y + 3z = - 10
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = \dfrac{{2y - 1}}{3}\\
z = \dfrac{{4y + 1}}{3}\\
\dfrac{{2y - 1}}{3} - 2y + 3.\dfrac{{4y + 1}}{3} = - 10
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = \dfrac{{2y - 1}}{3}\\
z = \dfrac{{4y + 1}}{3}\\
\dfrac{{2y - 1 - 6y + 12y + 3 + 30}}{3} = 0
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = \dfrac{{2y - 1}}{3}\\
z = \dfrac{{4y + 1}}{3}\\
\dfrac{{8y + 32}}{{30}} = 0
\end{array} \right.\\
\to \left\{ \begin{array}{l}
y = - 4\\
x = - 3\\
z = - 5
\end{array} \right.
\end{array}\)
