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г) \( \left\{\begin{array}{l}5(x-y)=10 \\ 3 x-7 y=20-(x+3 y)\end{array}\right. \)

Ask by Estrada Salinas. in Turkey
Nov 23,2024

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Система уравнений не имеет решения.

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Solve the system of equations \( 5(x-y)=10;3x-7y=20-(x+3y) \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}5\left(x-y\right)=10\\3x-7y=20-\left(x+3y\right)\end{array}\right.\) - step1: Calculate: \(\left\{ \begin{array}{l}5\left(x-y\right)=10\\3x-7y=20-x-3y\end{array}\right.\) - step2: Solve the equation: \(\left\{ \begin{array}{l}5\left(x-y\right)=10\\x=5+y\end{array}\right.\) - step3: Substitute the value of \(x:\) \(5\left(5+y-y\right)=10\) - step4: Simplify: \(25=10\) - step5: Calculate: \(\left\{ \begin{array}{l}x \in \varnothing \\y \in \varnothing \end{array}\right.\) - step6: Rewrite: \((x, y) \in \varnothing\) Система уравнений \( \left\{\begin{array}{l}5(x-y)=10 \\ 3x-7y=20-(x+3y)\end{array}\right. \) не имеет решения.

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Хорошо, давайте решим систему уравнений: 1. Первое уравнение: \(5(x - y) = 10\). Разделим обе стороны на 5: \[ x - y = 2 \quad (1) \] 2. Второе уравнение: \(3x - 7y = 20 - (x + 3y)\). Раскроем скобки: \[ 3x - 7y = 20 - x - 3y \] Переместим все элементы на одну сторону: \[ 3x + x - 7y + 3y = 20 \] Упростим: \[ 4x - 4y = 20 \quad (2) \] Делим обе стороны на 4: \[ x - y = 5 \quad (3) \] Теперь у нас есть две упрощенные системы уравнений: \[ \begin{cases} x - y = 2 \quad (1) \\ x - y = 5 \quad (3) \end{cases} \] Однако, тут мы видим, что \(x - y\) не может одновременно быть равным 2 и 5, что означает, что система уравнений не имеет решений. Уравнения несовместны.

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