Решите систему уравнений: 2x/5=1+y/2; 2x/5+y=-2.

Ответ:

\[\left\{ \begin{matrix} \frac{2x}{5} = 1 + \frac{y}{2}\ \ \ \ | \cdot 10 \\ \frac{2x}{5} + y = - 2\ \ \ \ | \cdot 5\ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} 2 \cdot 2x = 10 + 5y \\ 2x + 5y = - 10\ \ \ \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} 4x - 5y = 10\ \ \ \ \ \ (1) \\ 2x + 5y = - 10\ \ \ (2) \\ \end{matrix} \right.\ \]

\[(1) + (2) \Longrightarrow 6x = 0\]

\[\left\{ \begin{matrix} 6x = 0\ \ \ \ \ \ \ \ \ \ \ \\ \frac{2x}{5} + y = - 2 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} x = 0\ \ \ \ \ \ \ \ \ \ \ \ \\ y = - 2 - \frac{2x}{5} \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} x = 0\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ y = - 2 - \frac{2 \cdot 0}{5} \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} x = 0\ \ \ \\ y = - 2 \\ \end{matrix} \right.\ \]

\[Ответ:(0;\ - 2).\]