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The following system of linear equations 2x + 3y + 2z = 9 3x + 2y + 2z = 9 x − y + 4z = 8 (1) has a solution (α, β, γ) satisfying α + β^2 + γ^3 = 12 (2) has infinitely many solutions (3) does not have any solution (4) has a unique solution

1. has a solution (α, β, γ) satisfying α + β^2 + γ^3 = 12
2. has infinitely many solutions
3. does not have any solution
4. has a unique solution

Correct answer: has a unique solution

Solution

The system of equations is consistent and independent, meaning that there is exactly one solution that satisfies all three equations simultaneously, which confirms that it has a unique solution.

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