\(\begin{array}{l}
a)\,\,\left\{ \begin{array}{l}
{x^2} + {y^2} = 13\\
3{x^2} - 2{y^2} =  - 6
\end{array} \right.\,\,\,\,\,\,\,\left( 1 \right)\\
Dat\;{x^2} = a;\,\,{y^2} = b\,\,\,\,\left( {a,\,b\,\, \ge 0} \right)\\
\left( 1 \right) \Leftrightarrow \left\{ \begin{array}{l}
a + b = 13\\
3a - 2b =  - 6
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
a = 13 - b\\
3.\left( {13 - b} \right) - 2b =  - 6
\end{array} \right.\\
 \Leftrightarrow \left\{ \begin{array}{l}
a = 13 - b\\
39 - 3b - 2b =  - 6
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
a = 13 - b\\
 - 5b =  - 45
\end{array} \right.\\
 \Leftrightarrow \left\{ \begin{array}{l}
a = 13 - 9\\
b = 9
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
a = 4\\
b = 9
\end{array} \right.\,\,\,\left( {tmdk} \right)\\
 \Leftrightarrow \left\{ \begin{array}{l}
{x^2} = 4\\
{y^2} = 9
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
\left[ \begin{array}{l}
x =  - 2\\
x = 2
\end{array} \right.\\
\left[ \begin{array}{l}
y =  - 3\\
y = 3
\end{array} \right.
\end{array} \right.\\
Vay\,\,S = \left\{ {\left( { - 2; - 3} \right);\left( { - 2;3} \right);\left( {2; - 3} \right);\left( {2;3} \right)} \right\}.\\
b)\,\,\left\{ \begin{array}{l}
\left| x \right| + 4\left| y \right| = 18\\
3\left| x \right| + \left| y \right| = 10
\end{array} \right.\,\,\,\,\,\,\,\left( 2 \right)\\
Dat\;\left| x \right| = a;\,\,\left| y \right| = b\,\,\,\,\left( {a,\,b\,\, \ge 0} \right)\\
\left( 1 \right) \Leftrightarrow \left\{ \begin{array}{l}
a + 4b = 18\\
3a + b = 10
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
a = 18 - 4b\\
3.\left( {18 - 4b} \right) + b = 10
\end{array} \right.\\
 \Leftrightarrow \left\{ \begin{array}{l}
a = 18 - 4b\\
54 - 12b + b = 10
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
a = 18 - 4b\\
 - 11b =  - 44
\end{array} \right.\\
 \Leftrightarrow \left\{ \begin{array}{l}
a = 18 - 4.4\\
b = 4
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
a = 2\\
b = 4
\end{array} \right.\,\,\,\left( {tmdk} \right)\\
 \Leftrightarrow \left\{ \begin{array}{l}
\left| x \right| = 2\\
\left| y \right| = 4
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
\left[ \begin{array}{l}
x =  - 2\\
x = 2
\end{array} \right.\\
\left[ \begin{array}{l}
y =  - 4\\
y = 4
\end{array} \right.
\end{array} \right.\\
Vay\,\,S = \left\{ {\left( { - 2; - 4} \right);\left( { - 2;4} \right);\left( {2; - 4} \right);\left( {2;4} \right)} \right\}.
\end{array}\)