When solving simultaneous equations with a linear and quadratic equation, there will usually be two pairs of answers.

You construct a generalized linear model by deciding on response and explanatory variables for your data and choosing an appropriate link function and response probability distribution. Some examples ...

George Mackiw, The Linear Group SL (2, 3) as a Source of Examples, The Mathematical Gazette, Vol. 81, No. 490 (Mar., 1997), pp. 64-67 ...