$$2x + 2y - z = 2\pmod {3}$$

$$-x - 4y - 2z= 4\pmod {3}$$ I am lost in this... For simple equations I used Euclidean Algorithm. But in this problem I dont really know how to use this algorithm...

  • $\begingroup$ A general strategy for solving linear Diophantine systems is to compute the Smith normal form of the system. See en.m.wikipedia.org/wiki/Diophantine_equation $\endgroup$ – Teddan the Terran Oct 19 at 9:42
  • $\begingroup$ Exactly the way you solve it over rationals. $\endgroup$ – metamorphy Oct 19 at 10:01
  • 2
    $\begingroup$ Multiply the first equation by $2$ and subtract it from the second. $\endgroup$ – The Demonix _ Hermit Oct 19 at 10:11

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