If the determinant of the coefficient matrix of a linear system is 0, then the system has no unique solution. Otherwise, the system has 1 unique solution.Does the following linear system have a unique solution? 2x + 3y = 9-4x - 6y = 2

The coefficient matrix is [[2, 3], [-4, -6]], and its determinant is 2(-6) − 3(-4) = 0. Therefore, the system does not have a unique solution; in fact, the equations are inconsistent, so the correct choice is “no unique solution.”

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