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Home » $$ 0 = x^2 - 4x - 3 $$ - DNSFLEX

$$ 0 = x^2 - 4x - 3 $$ - DNSFLEX

📅 March 12, 2026 👤 scraface

Mar 12, 2026

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Substitute into (2):
-3(1 - 2y) + 2z = 5 \Rightarrow -3 + 6y + 2z = 5 \Rightarrow 6y + 2z =...
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 $
\langle 1, 0, 4 \rangle \times \langle 2, -1, 3 \rangle = \langle (0)(...
Thus, the general solution is a line, but a particular solution is:
\boxed{\langle 1, 0, 4 \rangle}

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