Question

$$27-6X=p(x-2)+q(x+1)$$

Solve for p (complex solution)

$\left\{\begin{matrix}p=-\frac{qx+q+6X-27}{x-2}\text{, }&x\neq 2\\p\in \mathrm{C}\text{, }&X=\frac{9-q}{2}\text{ and }x=2\end{matrix}\right.$

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Solve for X

$X=\frac{-q\left(x+1\right)-p\left(x-2\right)+27}{6}$

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Solve for p

$\left\{\begin{matrix}p=-\frac{qx+q+6X-27}{x-2}\text{, }&x\neq 2\\p\in \mathrm{R}\text{, }&X=\frac{9-q}{2}\text{ and }x=2\end{matrix}\right.$

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