Exercise 1.

Solve in ${\mathbb{Z}}$ the following equations or systems of equations.

1. $2 x \equiv 2 \mod{6}$ , with unknown $x$ ,
2. $5 x \equiv 2 \mod{6}$ , with unknown $x$ ,
3. $3x + 2y = 5$ , with unknown $(x,y)$ ,
4. $12x + 15y = 14$ , with unknown $(x,y)$ ,
5. $\left\{ \begin{array}{rccl} x & \equiv & 2 & \mod{3} \\ x & \equiv & 4 & \mod{5} \\ \end{array} \right.$

Answer 1