Đáp án:
\[x = y = 1\]
Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
\left\{ \begin{array}{l}
\left| {x - 1} \right| + \left| {y - 2} \right| = 1\\
\left| {x - 1} \right| + 3y = 3
\end{array} \right.\,\,\,\,\,\,\,\left( * \right)\\
TH1:\,\,\,y \ge 2 \Rightarrow y - 2 \ge 0 \Leftrightarrow \left| {y - 2} \right| = y - 2\\
\left( * \right) \Leftrightarrow \left\{ \begin{array}{l}
\left| {x - 1} \right| + y - 2 = 1\\
\left| {x - 1} \right| + 3y = 3
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
\left| {x - 1} \right| + y = 3\\
\left| {x - 1} \right| + 3y = 3
\end{array} \right.\\
\Rightarrow \left( {\left| {x - 1} \right| + 3y} \right) - \left( {\left| {x - 1} \right| + y} \right) = 3 - 3\\
\Leftrightarrow 2y = 0\\
\Leftrightarrow y = 0\,\,\,\,\,\left( {L,\,\,\,y \ge 2} \right)\\
TH1:\,\,y < 2 \Leftrightarrow y - 2 < 0 \Leftrightarrow \left| {y - 2} \right| = 2 - y\\
\left( * \right) \Leftrightarrow \left\{ \begin{array}{l}
\left| {x - 1} \right| + 2 - y = 1\\
\left| {x - 1} \right| + 3y = 3
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
\left| {x - 1} \right| - y = - 1\\
\left| {x - 1} \right| + 3y = 3
\end{array} \right.\\
\Rightarrow \left( {\left| {x - 1} \right| + 3y} \right) - \left( {\left| {x - 1} \right| - y} \right) = 3 - \left( { - 1} \right)\\
\Leftrightarrow 4y = 4\\
\Leftrightarrow y = 1\,\,\,\left( {t/m} \right)\\
\Rightarrow \left| {x - 1} \right| = 0 \Leftrightarrow x = 1
\end{array}\)
Vậy \(x = y = 1\)
