Đáp án:
\(\left[ \begin{array}{l}
m = 15\\
m = - \dfrac{6}{{17}}
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
\left\{ \begin{array}{l}
x = y + 5\\
m\left( {y + 5} \right) + \left( {m - 1} \right)y = 8m + 13\left( 1 \right)
\end{array} \right.\\
\left( 1 \right) \to my + 5m + \left( {m - 1} \right)y = 8m + 13\\
\to \left( {2m - 1} \right)y = 3m + 13\\
\to y = \dfrac{{3m + 13}}{{2m - 1}}\\
\to x = \dfrac{{3m + 13}}{{2m - 1}} + 5 = \dfrac{{3m + 13 + 10m - 5}}{{2m - 1}}\\
= \dfrac{{13m + 8}}{{2m - 1}}\\
DK:m \ne \dfrac{1}{2}\\
Do:x.y = 14\\
\to \dfrac{{13m + 8}}{{2m - 1}}.\dfrac{{3m + 13}}{{2m - 1}} = 14\\
\to \left( {13m + 8} \right)\left( {3m + 13} \right) = 14{\left( {2m - 1} \right)^2}\\
\to 39{m^2} + 193m + 104 = 14\left( {4{m^2} - 4m + 1} \right)\\
\to 39{m^2} + 193m + 104 = 56{m^2} - 56m + 14\\
\to 17{m^2} - 249m - 90 = 0\\
\to \left[ \begin{array}{l}
m = 15\\
m = - \dfrac{6}{{17}}
\end{array} \right.
\end{array}\)
