In this guide, we have solved linear systems using three methods: by graphing, substitution, and elimination. When solving nonlinear systems, we typically choose the substitution method, however, sometimes the other methods work just as well. Remember that to solve a system of equations means to find the common points - if they exist. Given a system of equations consisting of a circle and a line then there can be three possibilities for solutions. Remember that solutions to a system are ordered pairs (x, y). These will be the points where they intersect.
Solve the nonlinear systems.
Given a circle and a parabola there are five possibilities for solutions.
These nonlinear systems given algebraically might look like:
To find the points in common, we will usually use the substitution method. But, as in this case, the graphing and elimination method work just as well.
Certainly there are many ways to solve these problems. Experiment with other methods and see if you obtain the same results.