ГДЗ по алгебре 7 класс Макарычев ФГОС Задание 1090

\[\boxed{\text{1090.}\text{\ }еуроки - ответы\ на\ пятёрку}\]

\[\textbf{а)}\ \left\{ \begin{matrix} 5x - 4y = 16 \\ x - 2y = 6\ \ \ \ \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} x = 6 + 2y\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (2) \\ 5 \cdot (6 + 2y) - 4y = 16\ \ \ (1) \\ \end{matrix} \right.\ \]

\[(1)\ 30 + 10y - 4y = 16\]

\[6y = - 14\]

\[y = - \frac{14}{6} = - \frac{7}{3} = - 2\frac{1}{3}\]

\[(2)\ \ x = 6 - \frac{2 \cdot 7}{3} = 6 - \frac{14}{3}\]

\[x = \frac{18}{3} - \frac{14}{3} = \frac{4}{3} = 1\frac{1}{3}\]

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

\[\textbf{б)}\ \left\{ \begin{matrix} 20x - 15y = 100\ \ \ \ |\ :5 \\ 3x - y = 6\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} y = 3x - 6\ \ \ \\ 4x - 3y = 20 \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} y = 3x - 6\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (2) \\ 4x - 3 \cdot (3x - 6) = 20\ \ \ \ \ (1) \\ \end{matrix} \right.\ \]

\[(1)\ \ \ 4x - 9x + 18 = 20\]

\[- 5x = 2\]

\[x = - \frac{2}{5} = - 0,4\]

\[(2)\ \ y = 3 \cdot ( - 0,4) - 6\]

\[y = - 1,2 - 6 = - 7,2\]

\[Ответ:\ \ ( - 0,4;\ \ - 7,2).\]