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what is a trade triangle - Moon Smoking

📅 May 14, 2026 👤 scraface

May 14, 2026

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📌 From (3): \( 8a + 4b + 2c = 9 \) → divide by 2: \( 4a + 2b + c = 4.5 \)

📌 From (4): \( 27a + 9b + 3c = 18 \) → divide by 3: \( 9a + 3b + c = 6 \)

📌 Now add (1) and \( 4a + 2b + c = 4.5 \):

📌 Add \( (-a + b - c) + (4a + 2b + c) = 3 + 4.5 \Rightarrow 3a + 3b = 7.5 \Rightarrow a + b = 2.5 \) → (A)

📌 Now subtract \( (4a + 2b + c) \) from \( 9a + 3b + c \):

📌 Now solve (A) and (B):

📌 From (A): \( b = 2.5 - a \)

📌 Substitute into (B): \( 5a + (2.5 - a) = 1.5 \Rightarrow 4a + 2.5 = 1.5 \Rightarrow 4a = -1 \Rightarrow a = -\frac{1}{4} \)

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