### Groebner basis to solve linear system of equations

I am trying to solve a linear system of equation modulo some prime $p$. I have a matrix which gives me the coefficients of the polynomials (i.e., first row would be ($a, c, b, d$) for $ax+by+cz+d =0$). I would usually use solve_right(), writing my system as $Ax=b$ mod $p$, but I am intrigued by the use of Groebner basis. I have read about their implementation but I am confused at the notion of ideal to define before solving the system. I would like to solve the system in the ring $Z/pZ$. Also, can I feed a matrix to the function or should I first convert the matrix in a bunch of equations ?
Any clarification would be welcome !