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The following system of linear equations. \(\begin{aligned}& 2 x+3 y+2 z=9 \\& 3 x+2 y+2 z=9 \\& x-y+4 z=8\end{aligned}\…

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The following system of linear equations.
\(\begin{aligned}& 2 x+3 y+2 z=9 \\& 3 x+2 y+2 z=9 \\& x-y+4 z=8\end{aligned}\)

[JEE Main 2021, 25 Feb (Shift 2)]

a

has a unique solution

b

has a solution \((\alpha, \beta, \gamma)\) satisfying \(\alpha+\beta^2+\gamma^3=12\)

c

has infinitely many solutions

d

does not have any solution

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