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The following system of linear equations $3x + 3y + 2z = 9$, $3x + 2y + 2z = 9$, $x - y + 4z = 8$
(1) does not have any solution
(2) has a unique solution
(3) has a solution $(\alpha, \beta, \gamma)$ satisfying $\alpha + \beta^2 + \gamma^3 = 12$
(4) has infinitely many solutions
BETA
