Đáp án:
a) Hệ phương trình vô nghiệm
Giải thích các bước giải:
\(\begin{array}{l}
a)\left\{ \begin{array}{l}
9x - 6y = 4\\
3\left( {4x - 3y} \right) = - 3x + y + 7
\end{array} \right.\\
\to \left\{ \begin{array}{l}
9x - 6y = 4\\
12x - 9y = - 3x + y + 7
\end{array} \right.\\
\to \left\{ \begin{array}{l}
9x - 6y = 4\\
15x - 10y = 7
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = \dfrac{{6y + 4}}{9}\\
15\left( {\dfrac{{6y + 4}}{9}} \right) - 10y = 7
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = \dfrac{{6y + 4}}{9}\\
\dfrac{{30x + 20 - 30y - 21}}{3} = 0
\end{array} \right.\\
\to \left\{ \begin{array}{l}
0y = 1\left( {vô lý} \right)\\
x = \dfrac{{6y + 4}}{9}
\end{array} \right.
\end{array}\)
⇒ Hệ phương trình vô nghiệm
\(\begin{array}{l}
b)\left\{ \begin{array}{l}
3x + 3 + 2y = - x\\
5x + 5y = - 3x + y - 5
\end{array} \right.\\
\to \left\{ \begin{array}{l}
4x + 2y = - 3\\
8x + 4y = - 5
\end{array} \right.\\
\to \left\{ \begin{array}{l}
- 8x - 4y = - 6\\
8x + 4y = - 5
\end{array} \right.\\
\to \left\{ \begin{array}{l}
0x = - 11\left( {vô lý} \right)\\
8x + 4y = - 5
\end{array} \right.
\end{array}\)
⇒ Hệ phương trình vô nghiệm
\(\begin{array}{l}
c)\left\{ \begin{array}{l}
4x + 6y = 6x - 9y + 10\\
4x - 3y = 24y - 8x + 3
\end{array} \right.\\
\to \left\{ \begin{array}{l}
2x - 15y = - 10\\
12x - 27y = 3
\end{array} \right.\\
\to \left\{ \begin{array}{l}
- 12x + 90y = - 60\\
12x - 27y = 3
\end{array} \right.\\
\to \left\{ \begin{array}{l}
63y = - 63\\
12x - 27y = 3
\end{array} \right.\\
\to \left\{ \begin{array}{l}
y = - 1\\
x = - 2
\end{array} \right.
\end{array}\)
