Đáp án:
e) \(\left\{ \begin{array}{l}
y = \dfrac{{ - \sqrt 5 - 1}}{3}\\
x = \dfrac{{ - 10 + \sqrt 5 }}{{15}}
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
a)\left\{ \begin{array}{l}
- 15x - 9y = - 57\\
2x + 9y = 31
\end{array} \right.\\
\to \left\{ \begin{array}{l}
- 13x = - 26\\
2x + 9y = 31
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = 2\\
y = 3
\end{array} \right.\\
b)\left\{ \begin{array}{l}
6x - 8y = 20\\
- 6x + 8y = - 19
\end{array} \right.\\
\to \left\{ \begin{array}{l}
0x + 0y = 1\left( {vô lý} \right)\\
- 6x + 8y = - 19
\end{array} \right.
\end{array}\)
⇒ Hệ phương trình vô nghiệm
\(\begin{array}{l}
c)\left\{ \begin{array}{l}
15x + 8y = 46\\
5x - 3y = 4
\end{array} \right.\\
\to \left\{ \begin{array}{l}
15x + 8y = 46\\
- 15x + 9y = - 12
\end{array} \right.\\
\to \left\{ \begin{array}{l}
17y = 34\\
5x - 3y = 4
\end{array} \right.\\
\to \left\{ \begin{array}{l}
y = 2\\
x = 2
\end{array} \right.\\
d)\left\{ \begin{array}{l}
5x - 4y = 20\\
5x - 4y = 20
\end{array} \right.\\
\to \left\{ \begin{array}{l}
0x + 0y = 0\\
5x - 4y = 20
\end{array} \right.
\end{array}\)
⇒ Hệ phương trình vô số nghiệm
\(\begin{array}{l}
e)\left\{ \begin{array}{l}
5x - 2\sqrt 5 y = \sqrt 5 \\
5x + \sqrt 5 y = - 5
\end{array} \right.\\
\to \left\{ \begin{array}{l}
3\sqrt 5 y = - 5 - \sqrt 5 \\
5x - 2\sqrt 5 y = \sqrt 5
\end{array} \right.\\
\to \left\{ \begin{array}{l}
y = \dfrac{{ - \sqrt 5 - 1}}{3}\\
x = \dfrac{{ - 10 + \sqrt 5 }}{{15}}
\end{array} \right.
\end{array}\)
