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Home » Therefore, the solution is \( x = \frac32 \). - Dachbleche24

Therefore, the solution is \( x = \frac32 \). - Dachbleche24

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 Question: A museum curator arranges two exhibit pathways modeled by the lines $ y = 4x - 5 $ and $ 2y + 3x = 10 $. Find their intersection point.

📌 Solution: Substitute $ y = 4x - 5 $ into the second equation: $ 2(4x - 5) + 3x = 10 $. Simplify: $ 8x - 10 + 3x = 10 \Rightarrow 11x = 20 \Rightarrow x = \frac{20}{11} $. Substitute back: $ y = 4\left(\frac{20}{11}\right) - 5 = \frac{80}{11} - \frac{55}{11} = \frac{25}{11} $.

📌 \boxed{\left( \frac{20}{11}, \frac{25}{11} \right)}

📌 Question: Expand the product $ (5a - 3b)(2a + 7b) $.

📌 Solution: Use the distributive property:

📌 $ 5a \cdot 2a = 10a^2 $,

📌 $ 5a \cdot 7b = 35ab $,

📌 $ -3b \cdot 2a = -6ab $,

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