Problem
NT-B2-M09-P003 An Incompatible System
#3
★★☆☆☆ Level 2 of 5
Prove that the system \(x\equiv 2\pmod 6\), \(x\equiv 3\pmod 9\) has no solutions.
Compare the residues modulo the common divisor of the moduli.
If \(x\equiv 2\pmod 6\), then \(x\equiv 2\pmod 3\). If \(x\equiv 3\pmod 9\), then \(x\equiv 0\pmod 3\). The same integer cannot have two different residues modulo \(3\). Therefore there are no solutions.
A minimal compatibility check.