Решите уравнение: |x+3y-5|+(7x-6y+4)^2=0.

\[\left\{ \begin{matrix} x + 3y - 5 = 0\ \ \ | \cdot 2 \\ 7x - 6y + 4 = 0\ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} 2x + 6y - 10 = 0 \\ 7x - 6y + 4 = 0\ \ \ \\ \end{matrix} + \right.\ \text{\ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} 9x = 6 \\ y = \frac{4 + 7x}{6} \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} x = \frac{2}{3}\text{\ \ \ } \\ y = \frac{13}{9} \\ \end{matrix} \right.\ \]

\[Ответ:\left( \frac{2}{3};\ 1\frac{4}{9} \right).\]