# Resolve this system of linear equations in Z/Z7 and write 8 possible solutions.

$$\left\{ \begin{array}{l} x_1 &+&2x_2&+&3x_5&&&&&=& 3;\\ 2x_1 &+&4x_2&+&3x_3&+&6x_4&+&x_5 &=& 5;\\ 3x_1 &+&6x_2&+&2x_3&+&4x_4&+&x_5 &=& 6;\\ 4x_1 &+&x_2&+&3x_3&+&6x_4&&&=&4. \end{array} \right.$$

I transformed this matrix in normal form, then i calculated 49 possible solutions. But how can I write down 8 of 49 of this possible solutions?