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3. \( \left\{\begin{array}{l}-3 x+y=5 \\ 6 x-2 y=9\end{array}\right. \)

Ask by Wilson Warren. in the United States
Mar 14,2025

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The system of equations has no solution.

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To solve the given system of equations, let's rewrite them for clarity. We have: 1. \(-3x + y = 5\) 2. \(6x - 2y = 9\) From the first equation, we can express \(y\) in terms of \(x\): \(y = 3x + 5\). Now, let’s substitute \(y\) in the second equation: \(6x - 2(3x + 5) = 9\). This simplifies to: \(6x - 6x - 10 = 9\), which leads to \(-10 = 9\). This inconsistency means that the system has no solution, indicating the lines represented by these equations are parallel. A common tip is always to check for inconsistencies like this, which can save time and effort in solving systems! Remember, parallel lines never meet, which means you’ll never find a solution that satisfies both equations at the same time.

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