Đáp án:
f. \(\left[ \begin{array}{l}
y = 9\\
y = - 9
\end{array} \right. \to \left[ \begin{array}{l}
x = 12\\
x = - 12
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
a.\left\{ \begin{array}{l}
x = \dfrac{3}{5}y\\
z = - \dfrac{2}{5}y\\
5x - y + 3z = - 16
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = \dfrac{3}{5}y\\
z = - \dfrac{2}{5}y\\
5.\dfrac{3}{5}y - y + 3.\left( { - \dfrac{2}{5}y} \right) = - 16
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = \dfrac{3}{5}y\\
z = - \dfrac{2}{5}z\\
\dfrac{4}{5}y = - 16
\end{array} \right.\\
\to \left\{ \begin{array}{l}
y = - 20\\
x = - 12\\
z = 8
\end{array} \right.\\
b.\left\{ \begin{array}{l}
x = - \dfrac{2}{3}y\\
z = \dfrac{3}{4}y\\
- \dfrac{2}{3}y + y + \dfrac{3}{4}y = \dfrac{{26}}{5}
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = - \dfrac{2}{3}y\\
z = \dfrac{3}{4}y\\
\dfrac{{13}}{{12}}y = \dfrac{{26}}{5}
\end{array} \right.\\
\to \left\{ \begin{array}{l}
y = \dfrac{{24}}{5}\\
x = - \dfrac{{16}}{5}\\
z = \dfrac{{18}}{5}
\end{array} \right.\\
c.\left\{ \begin{array}{l}
x = \dfrac{3}{2}y\\
z = \dfrac{5}{7}y\\
3.\dfrac{3}{2}y - 7y + 5.\dfrac{5}{7}y = 30
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = \dfrac{3}{2}y\\
z = \dfrac{5}{7}y\\
\dfrac{{15}}{{14}}y = 30
\end{array} \right.\\
\to \left\{ \begin{array}{l}
y = 28\\
x = 42\\
z = 20
\end{array} \right.\\
d.\left\{ \begin{array}{l}
3x + 9 = 5y - 10\\
7y - 14 = 3z - 3\\
3x + 5y - 7z = 32
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = \dfrac{{5y - 19}}{3}\\
z = \dfrac{{7y - 11}}{3}\\
3.\dfrac{{5y - 19}}{3} + 5y - 7.\dfrac{{7y - 11}}{3} = 32
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = \dfrac{{5y - 19}}{3}\\
z = \dfrac{{7y - 11}}{3}\\
5y - 19 + 5y - \dfrac{{49y - 77}}{3} = 32
\end{array} \right.\\
\to \left\{ \begin{array}{l}
\dfrac{{30y - 57 - 49y + 77 - 96}}{3} = 0\\
x = \dfrac{{5y - 19}}{3}\\
z = \dfrac{{7y - 11}}{3}
\end{array} \right.\\
\to \left\{ \begin{array}{l}
- 19y = 76\\
x = \dfrac{{5y - 19}}{3}\\
z = \dfrac{{7y - 11}}{3}
\end{array} \right.\\
\to \left\{ \begin{array}{l}
y = - 4\\
x = - 13\\
z = - 13
\end{array} \right.\\
e.\left\{ \begin{array}{l}
x = \dfrac{4}{5}y\\
\dfrac{4}{5}y.y = 80
\end{array} \right.\\
\to \left\{ \begin{array}{l}
{y^2} = 100\\
x = \dfrac{4}{5}y
\end{array} \right.\\
\to \left[ \begin{array}{l}
y = 10\\
y = - 10
\end{array} \right. \to \left[ \begin{array}{l}
x = 8\\
x = - 8
\end{array} \right.\\
f.\left\{ \begin{array}{l}
x = \dfrac{4}{3}y\\
\dfrac{{16}}{9}{y^2} - {y^2} = 63
\end{array} \right.\\
\to \left\{ \begin{array}{l}
\dfrac{7}{9}{y^2} = 63\\
x = \dfrac{4}{3}y
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = \dfrac{4}{3}y\\
{y^2} = 81
\end{array} \right.\\
\to \left[ \begin{array}{l}
y = 9\\
y = - 9
\end{array} \right. \to \left[ \begin{array}{l}
x = 12\\
x = - 12
\end{array} \right.
\end{array}\)
