Đáp án:
2) m=8
Giải thích các bước giải:
\(\begin{array}{l}
1)\left\{ \begin{array}{l}
y = 13 - 2x\\
mx + 6\left( {13 - 2x} \right) = 8
\end{array} \right.\\
\to \left\{ \begin{array}{l}
y = 13 - 2x\\
mx + 78 - 12x = 8
\end{array} \right.\\
\to \left\{ \begin{array}{l}
y = 13 - 2x\\
\left( {m - 12} \right)x = - 70
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = \dfrac{{ - 70}}{{m - 12}}\\
y = 13 - 2.\dfrac{{ - 70}}{{m - 12}} = \dfrac{{13m - 156 + 140}}{{m - 12}}
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = \dfrac{{ - 70}}{{m - 12}}\\
y = \dfrac{{13m - 16}}{{m - 12}}
\end{array} \right.\\
DK:m \ne 12\\
Do:x + 3y = 14\\
\to \dfrac{{ - 70}}{{m - 12}} + 3.\dfrac{{13m - 16}}{{m - 12}} = 14\\
\to - 70 + 39m - 48 = 14m - 168\\
\to 25m = - 50\\
\to m = - 2\\
2)\left\{ \begin{array}{l}
y = 3x - 5\\
x + \left( {m + 2} \right)\left( {3x - 5} \right) = 12
\end{array} \right.\\
\to \left\{ \begin{array}{l}
y = 3x - 5\\
x + 3mx - 5m + 6x - 10 = 12
\end{array} \right.\\
\to \left\{ \begin{array}{l}
y = 3x - 5\\
\left( {7 + 3m} \right)x = 5m + 22
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = \dfrac{{5m + 22}}{{3m + 7}}\\
y = 3.\dfrac{{5m + 22}}{{3m + 7}} - 5 = \dfrac{{15m + 66 - 15m - 35}}{{3m + 7}}
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = \dfrac{{5m + 22}}{{3m + 7}}\\
y = \dfrac{{31}}{{3m + 7}}
\end{array} \right.\\
DK:m \ne - \dfrac{7}{3}\\
Do:4x + y = 9\\
\to 4.\dfrac{{5m + 22}}{{3m + 7}} + \dfrac{{31}}{{3m + 7}} = 9\\
\to 20m + 88 + 31 = 27m + 63\\
\to 7m = 56\\
\to m = 8
\end{array}\)
