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If b is equal to zero the system always has a solution x=y=z=0. If you assume that b is not equal to 0 the sentence "There are more than one integer values of a for which (...)" still remains false for the given system.
Linear Algebra Foundations #8 - Systems of Equations
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If b is equal to zero the system always has a solution x=y=z=0. If you assume that b is not equal to 0 the sentence "There are more than one integer values of a for which (...)" still remains false for the given system.