We saw that a system of two linear equations in three variables x, y and z represents two planes in R^3. Thus solving this system of two simultaneous equations is equivalent to finding out how (or whether) the two corresponding planes intersect each other. We saw that there are three possible outcomes: either they intersect in a line (in which case there are infinitely many solutions described by a single parameter), or they are in fact the same plane (in which case there are infinitely many solutions described by two parameters), or they are parallel (and not the same, in which case there are no solutions).