Exercise 1.

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

1. 2x $\equiv$ 2 mod6, with unknown x,
2. 5x $\equiv$ 2 mod6, with unknown x,
3. 3x + 2y = 5, with unknown (x, y),
4. 12x + 15y = 14, with unknown (x, y),
5. $\left\{\vphantom{ \begin{array}{rccl} x & \equiv & 2 & \mod{3} \\ x & \equiv & 4 & \mod{5} \\ \end{array} }\right.$$\begin{array}{rccl} x & \equiv & 2 & \mod{3} \\ x & \equiv & 4 & \mod{5} \\ \end{array}$

Answer 1