That depends on what question you have been asked concerning the two tangents. All by itself, a circle with two tangents is quite content, and isn't looking for a solution.
.. touches each circle in exactly one point on each circle. given any two circles where none is entirely inside or inside and tangent to the other, there are at most four straight lines that are...
I guess you mean simultaneous equations. There are three methods of solving these equations: graphing if the variables are x and y (though this is only an approximate method and should be avoided...