Giải thích các bước giải:
Áp dụng tính chất dãy tỉ số bằng nhau ta có:
\(\begin{array}{l}
a,\\
5x = 8y \Leftrightarrow \dfrac{x}{8} = \dfrac{y}{5} \Leftrightarrow \dfrac{x}{8} = \dfrac{{2.y}}{{2.5}} \Leftrightarrow \dfrac{{ - x}}{{ - 8}} = \dfrac{{2y}}{{10}}\\
\dfrac{{ - x}}{{ - 8}} = \dfrac{{2y}}{{10}} = \dfrac{{ - x + 2y}}{{\left( { - 8} \right) + 10}} = \dfrac{{ - 12}}{2} = - 6\\
\Rightarrow \left\{ \begin{array}{l}
\dfrac{{ - x}}{{ - 8}} = - 6\\
\dfrac{{2y}}{{10}} = - 6
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
x = - 48\\
y = - 30
\end{array} \right.\\
b,\\
\dfrac{{2x - 3}}{5} = \dfrac{{3y + 2}}{7} = \dfrac{{z - 1}}{3}\\
\Leftrightarrow \dfrac{{2.\left( {2x - 3} \right)}}{{2.5}} = \dfrac{{2.\left( {3y + 2} \right)}}{{2.7}} = \dfrac{{7.\left( {z - 1} \right)}}{{7.3}}\\
\Leftrightarrow \dfrac{{4x - 6}}{{10}} = \dfrac{{6y + 4}}{{14}} = \dfrac{{7z - 7}}{{21}} = \dfrac{{\left( {4x - 6} \right) - \left( {6y + 4} \right) + \left( {7z - 7} \right)}}{{10 - 14 + 21}} = \dfrac{{\left( {4x - 6y + 7z} \right) - 17}}{{17}} = \dfrac{{68 - 17}}{{17}} = 3\\
\Rightarrow \left\{ \begin{array}{l}
\dfrac{{4x - 6}}{{10}} = 3\\
\dfrac{{6y + 4}}{{14}} = 3\\
\dfrac{{7z - 7}}{{21}} = 3
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
x = 9\\
y = \dfrac{{19}}{3}\\
z = 10
\end{array} \right.
\end{array}\)
