You won't be able to find a unique solution. It should be obvious that there are infinitely many vectors perpendicular to a given vector, so if you only want one you will have to pick arbitrarily.
So, solve for one of the variables in terms of the other, and then pick an arbitrary value for the second component to find the corresponding value for the first.
Or, if you want the general solution (i.e., all possible solutions), introduce a parameter (for example, let and then solve for in terms of ).
Does that make sense?