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Тип 13 № \( \underline{3294} \) (!) \( i \) Решите систему уравнений \( \left\{\begin{array}{l}3 x+y=1, \\ \frac{x+1}{3}-\frac{y}{5}=2 .\end{array}\right. \) Спрятать решение

Ask by Nichols Vaughan. in Russia
Mar 14,2025

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\( x = 2 \), \( y = -5 \).

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Чтобы решить данную систему уравнений, начнем с первого уравнения: \(3x + y = 1.\) Выразим \(y\): \(y = 1 - 3x.\) Теперь подставим это значение во второе уравнение: \(\frac{x + 1}{3} - \frac{(1 - 3x)}{5} = 2.\) Умножим на 15, чтобы избавиться от дробей: \(5(x + 1) - 3(1 - 3x) = 30.\) Раскроем скобки: \(5x + 5 - 3 + 9x = 30.\) Сложим подобные: \(14x + 2 = 30.\) Вычтем 2: \(14x = 28.\) Теперь разделим на 14: \(x = 2.\) Подставим \(x\) обратно в выражение для \(y\): \(y = 1 - 3(2) = 1 - 6 = -5.\) Таким образом, решение системы: \(x = 2,\) \(y = -5\).

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