§2. Приложения математики в реальной жизни — 5. Практико-ориентированные задачи — 74 — стр. 25

\(\left\{\begin{array}{l}3y - 2x = 10 \\ 7x + 5y = 27 \end{array}\right. \Leftrightarrow \left\{\begin{array}{c} x=\frac{3y-10}{2} \\ 7\left(\frac{3y-10}{2}\right) + 5y = 27 \end{array}\right. \Leftrightarrow \\ \Leftrightarrow \left\{\begin{array}{c} x = \frac{3y-10}{2} \\ 10.5y - 35 + 5y = 27 \end{array}\right. \Leftrightarrow \left\{\begin{array}{l} x=\frac{3y-10}{2} \\ 15.5y = 62 \end{array}\right. \Leftrightarrow \\ \Leftrightarrow \left\{\begin{array}{l} x = \frac{3 \cdot 4 - 10}{2} = 1 \\ y = \frac{62}{15.5} = \frac{124}{31} = 4 \end{array}\right. \Leftrightarrow \left\{\begin{array}{l} x=1 \\ y=4 \end{array}\right.\).

\(\left\{\begin{array}{l}0.4x - 0.2y = \frac{0.4}{0.2} \\ x + 11y = 12.5 \end{array}\right. \Leftrightarrow \left\{\begin{array}{c} 2x - y = 2 \\ x = 12.5 - 11y \end{array}\right. \Leftrightarrow \\ \Leftrightarrow \left\{\begin{array}{c}2(12.5 - 11y) - y = 2 \\x = 12.5 - 11y\end{array}\right. \Leftrightarrow \left\{\begin{array}{c}25 - 22y - y = 2 \\x = 12.5 - 11y \end{array}\right. \Leftrightarrow \\ \Leftrightarrow \left\{\begin{array}{c}-23y = -23 \\x = 12.5 - 11y\end{array}\right. \Leftrightarrow \left\{\begin{array}{c}y = 1 \\x = 12.5 - 11 = 1.5\end{array}\right. \Leftrightarrow \left\{\begin{array}{c} x=1.5 \\y=1\end{array}\right.\).