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Home » 8a + 4b + 2c + d = 5 \\ - AMAZONAWS

8a + 4b + 2c + d = 5 \\ - AMAZONAWS

📅 March 6, 2026 👤 scraface

Mar 06, 2026

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📌 -x - 2y = -1 \Rightarrow x = 1 - 2y

📌 Substitute into (2):

📌 -3(1 - 2y) + 2z = 5 \Rightarrow -3 + 6y + 2z = 5 \Rightarrow 6y + 2z = 8 \Rightarrow 3y + z = 4

📌 This matches equation (1), so consistent. Use (1): $ z = 4 - 3y $

📌 Now express $ x = 1 - 2y $, $ z = 4 - 3y $ — so in terms of $ y $,

📌 \mathbf{v} = \langle 1 - 2y, y, 4 - 3y \rangle

📌 For a particular solution, choose $ y = 0 $:

📌 Then $ x = 1 $, $ z = 4 $, so $ \mathbf{v} = \langle 1, 0, 4 \rangle $

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b_4 = \frac{904518 - 97336}{1594323} = \frac{807182}{1594323}
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Set $ u^3 - 5u^2 + 6u = 0 $. Factor:
u(u^2 - 5u + 6) = 0 \Rightarrow u(u - 2)(u - 3) = 0
So $ u = 0, 2, $ or $ 3 $. Since $ x = u^2 $, the corresponding $ x $-...
$ u = 0 \Rightarrow x = 0 $
$ u = 2 \Rightarrow x = 4 $
$ u = 3 \Rightarrow x = 9 $

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