 Linear equation over a ring

A linear equation over a ring is an expression of the form: \[ a_1 x_1 + a_2 x_2 + \ldots + a_n x_n = b \] where \(a_1, a_2, \ldots, a_n\) and \(b\) are elements of a ring \(R\), and \(x_1, x_2, \ldots, x_n\) are variables that take values in the ring