Systems Involving Second Degree Equations

If a system of equations contains any equation that is not linear,
the system is called a nonlinear system
For example,

          

The solutions of such nonlinear systems may contain complex numbers, a+bi
We will assume that the replacement set for each variable is the set of complex numbers,
which includes the set of real numbers
The process of solving a nonlinear system of equations may produce numbers
that do not satisfy all of the equations of the nonlinear system
Such numbers are called extraneous solutions, or extraneous roots, of the system
It is important to check the derived solutions of any nonlinear system
in order to ensure that extraneous roots have not been introduced.

     See Example 1, pages 690 - 691, of the textbook


Solution by Substitution
The substitution method used to solve linear system
may be used to solve nonlinear systems

     See Examples 1 – 3, pages 690 – 693, of the textbook


Other Solution Methods

     Elimination –
                         see Example 4, pages 694 – 695, of the textbook
     Factoring and Substitution –
                         see Example 5, pages 695 - 696, of the textbook
     Graphic Approximation –
                         see Example 6, page 696, of the textbook


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