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.

Solve.