Решите систему уравнений способом подстановки: 5x-3y=1; x+2y=5.

\[\left\{ \begin{matrix} 5x - 3y = 1 \\ x + 2y = 5\ \ \ \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} x = 5 - 2y\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 5(5 - 2y) - 3y = 1 \\ \end{matrix} \right.\ \]

\[25 - 10y - 3y - 1 = 0\]

\[- 13y = - 24\]

\[y = \frac{24}{13} = 1\frac{11}{13}.\]

\[x = 5 - 2 \cdot \frac{24}{13} = 5 - \frac{48}{13} =\]

\[= 5 - 3\frac{9}{13} = 1\frac{4}{13}.\]

\[Ответ:\left( 1\frac{4}{13};1\frac{11}{13} \right).\]