Đáp án:
d. \(\left\{ \begin{array}{l}
y = \dfrac{{10}}{3}\\
x = 5\\
z = \dfrac{5}{3}
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
a.\left\{ \begin{array}{l}
\dfrac{x}{2} = \dfrac{y}{3} = \dfrac{z}{5}\\
x + 22y - 3z = 6
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = \dfrac{2}{3}y\\
z = \dfrac{5}{3}y\\
\dfrac{2}{3}y + 22y - 3.\dfrac{5}{3}y = 6
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = \dfrac{2}{3}y\\
z = \dfrac{5}{3}y\\
\dfrac{{53}}{3}y = 6
\end{array} \right.\\
\to \left\{ \begin{array}{l}
y = \dfrac{{18}}{{53}}\\
x = \dfrac{{12}}{{53}}\\
z = \dfrac{{36}}{{265}}
\end{array} \right.\\
b.\left\{ \begin{array}{l}
x = \dfrac{1}{2}y\\
3.\dfrac{1}{2}y - y = 25
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = \dfrac{1}{2}y\\
\dfrac{1}{2}y = 25
\end{array} \right.\\
\to \left\{ \begin{array}{l}
y = 50\\
x = 25
\end{array} \right.\\
c.\left\{ \begin{array}{l}
x = \dfrac{3}{5}y\\
\dfrac{3}{5}y.y = 135
\end{array} \right.\\
\to \left\{ \begin{array}{l}
{y^2} = 225\\
x = \dfrac{3}{5}y
\end{array} \right.\\
\to \left[ \begin{array}{l}
y = 15\\
y = - 15
\end{array} \right. \to \left[ \begin{array}{l}
x = 9\\
x = - 9
\end{array} \right.\\
d.\left\{ \begin{array}{l}
x = \dfrac{3}{2}y\\
z = \dfrac{2}{4}y\\
\dfrac{3}{2}y + y + \dfrac{1}{2}y = 10
\end{array} \right.\\
\to \left\{ \begin{array}{l}
3y = 10\\
x = \dfrac{3}{2}y\\
z = \dfrac{2}{4}y
\end{array} \right.\\
\to \left\{ \begin{array}{l}
y = \dfrac{{10}}{3}\\
x = 5\\
z = \dfrac{5}{3}
\end{array} \right.
\end{array}\)
