Giải thích các bước giải:
\(\begin{array}{l}
a.\left\{ \begin{array}{l}
x + y = 1\\
3x + \left( {m - 1} \right)y = 13\\
\left( {m - 1} \right)x + 12y = 24
\end{array} \right. \to \left\{ \begin{array}{l}
x = 1 - y\\
3 - 3y + \left( {m - 1} \right)y = 13\\
\left( {m - 1} \right)\left( {1 - y} \right) + 12y = 24
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = 1 - y\\
3 - 3y + my - y = 13\\
m - my - 1 + y + 12y = 24
\end{array} \right. \to \left\{ \begin{array}{l}
x = 1 - y\\
- 4y + my = 10\\
13y - my = 25 - m
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = 1 - y\\
9y = 35 - m\\
- 4y + my = 10
\end{array} \right. \to \left\{ \begin{array}{l}
x = 1 - y\\
m = 35 - 9y\\
- 4y + 35y - 9{y^2} = 10
\end{array} \right.\\
\to \left[ \begin{array}{l}
y = \frac{{31 + \sqrt {601} }}{{18}}\\
y = \frac{{31 - \sqrt {601} }}{{18}}
\end{array} \right. \to \left[ \begin{array}{l}
m = \frac{{39 - \sqrt {601} }}{2}\\
m = \frac{{39 + \sqrt {601} }}{2}
\end{array} \right.\\
b.\left\{ \begin{array}{l}
3x + \left( {m - 1} \right)y = 13\\
\left( {m - 1} \right)x + 12y = 24
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = \frac{{13 - \left( {m - 1} \right)y}}{3}\\
\left( {m - 1} \right).\frac{{13 - \left( {m - 1} \right)y}}{3} + 12y = 24\left( * \right)
\end{array} \right.\\
\left( * \right) \to 13m - 13 - \left( {{m^2} - 2m + 1} \right)y + 36y = 72\\
\to 13m - 13 - {m^2}y + 2my - y + 36y = 72\\
\to y = \frac{{85 - 13m}}{{35 + 2m - {m^2}}}\\
\to x = \frac{{13 - \left( {m - 1} \right)y}}{3} = \frac{{13 - \left( {m - 1} \right)\frac{{85 - 13m}}{{35 + 2m - {m^2}}}}}{3}\\
\to x = \frac{{13 - \frac{{85m - 85 - 13{m^2} + 13m}}{{35 + 2m - {m^2}}}}}{3}\\
= \frac{{455 + 26m - 13{m^2} - 98m + 85 + 13{m^2}}}{{3.\left( {35 + 2m - {m^2}} \right)}}\\
= \frac{{ - 72m + 540}}{{105 + 6m - 3{m^2}}}
\end{array}\)
