Giải thích các bước giải:
\(\begin{array}{l}
a)\left\{ \begin{array}{l}
x + 2y = 3\\
3x - 2y = 5
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
4x = 8\\
x + 2y = 3
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
x = 2\\
y = \dfrac{1}{2}
\end{array} \right.\\
b)\left\{ \begin{array}{l}
4x = m + 5\\
y = \dfrac{{3x - 5}}{2}
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
x = \dfrac{{m + 5}}{4}\\
y = \dfrac{{3m + 15 - 20}}{8}
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
x = \dfrac{{m + 5}}{4}\\
y = \dfrac{{3m - 5}}{8}
\end{array} \right.\\
c) - 3x + y = 2\\
\Leftrightarrow - 3\left( {\dfrac{{m + 5}}{4}} \right) + \dfrac{{3m - 5}}{8} = 2\\
\Leftrightarrow \dfrac{{ - 6m - 30 + 3m - 5}}{8} = 2\\
\Leftrightarrow - 3m - 35 = 16 \Leftrightarrow 3m = - 51 \Leftrightarrow m = 17\\
d){x^2} + {y^2} = \dfrac{{{{\left( {m + 5} \right)}^2}}}{{16}} + \dfrac{{{{\left( {3m - 5} \right)}^2}}}{{64}}\\
= \dfrac{1}{{64}}\left( {4{m^2} + 40m + 100 + 9{m^2} - 30m + 25} \right)\\
= \dfrac{1}{{64}}\left( {13{m^2} + 10m + 125} \right)\\
= \dfrac{1}{{823}}\left( {{m^2} + 2.\dfrac{5}{{13}}m + \dfrac{{25}}{{169}}} \right) + \dfrac{{21100}}{{139087}}\\
= \dfrac{1}{{823}}{\left( {m + \dfrac{5}{{13}}} \right)^2} + \dfrac{{21100}}{{139087}} \ge \dfrac{{21100}}{{139087}}\\
GTNN\dfrac{{21100}}{{139087}} \Leftrightarrow m = - \dfrac{5}{{13}}\\
e)\left\{ \begin{array}{l}
x < 0\\
y < 0
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
m + 5 < 0\\
3m - 5 < 0
\end{array} \right. \Leftrightarrow m < - 5
\end{array}\)
