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I did Gaussian elimination carefully and discovered that the coefficient matrix for the row reduced system of equations is invertible unless a = 2 or a = -1.
Then I checked that there is in fact no solution when a = -1. (We know b is not 0, because otherwise the given system of equations would always have a solution consisting of all zeros.)
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Linear Algebra Foundations #8 - Systems of Equations
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I did Gaussian elimination carefully and discovered that the coefficient matrix for the row reduced system of equations is invertible unless a = 2 or a = -1.
Then I checked that there is in fact no solution when a = -1. (We know b is not 0, because otherwise the given system of equations would always have a solution consisting of all zeros.)