ГДЗ по алгебре 7 класс Макарычев ФГОС Задание 1108

\[\boxed{\text{1108.}\text{\ }еуроки - ответы\ на\ пятёрку}\]

\[\textbf{а)}\ \left\{ \begin{matrix} 5 \cdot (x + 2y) - 3 = x + 5 \\ y + 4 \cdot (x - 3y) = 50\ \ \ \ \ \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} 5x + 10y - 3 = x + 5 \\ y + 4x - 12y = 50\ \ \ \ \ \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} 4x + 10y = 8\ \ | \cdot ( - 1) \\ - 11y + 4x = 50\ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} - 4x - 10y = - 8 \\ - 11y + 4x = 50 \\ \end{matrix} \right.\ ( + ) \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} - 21y = 42\ \ \ \ \\ 4x = 8 - 10y \\ \end{matrix} \right.\ \Longrightarrow\]

\[\left\{ \begin{matrix} y = - 2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 4x = 8 - 10 \cdot ( - 2) \\ \end{matrix} \right.\ \]

\[y = - 2\]

\[x = \frac{8 + 20}{4} = \frac{28}{4} = 7\]

\[Ответ:(7;\ - 2).\]

\[\textbf{б)}\ \left\{ \begin{matrix} 2,5 \cdot (x - 3y) - 3 = - 3x + 0,5 \\ 3 \cdot (x + 6y) + 4 = 9y + 19\ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} 2,5x - 7,5y - 3 + 3x = 0,5 \\ 3x + 18y + 4 - 9y = 19\ \ \ \ \ \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} 5,5x - 7,5y = 3,5\ \ \ |\ \ :5 \\ 3x + 9y = 15\ \ \ \ \ \ \ \ \ \ \ |\ :3 \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} 1,1x - 1,5y = 0,7\ \ | \cdot ( - 2) \\ x + 3y = 5\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} - 2,2x + 3y = - 1,4 \\ x + 3y = 5\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ ( - ) \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} - 3,2x = - 6,4 \\ 3y = 5 - x\ \ \ \ \\ \end{matrix} \right.\ \Longrightarrow\]

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

\[Ответ:(2;1).\]