A system of quadratic equations is a system where all equations are quadratic. They can be expressed as follows. The graphs to quadratic systems can have or infinitely many points of intersection. Thus, the number of solutions of a quadratic system is also or infinitely many.
Solve the system using substitution.
A quadratic system can also consist of quadratic inequalities, such asThe solution set to a system of quadratic inequalities is, similar to systems of linear inequalities, an entire region in the coordinate plane.
Next, graph the other inequality. Here, has the boundary The region corresponding to the solution set also lies inside the parabola.
The solutions to the system are solutions to both individual inequalities. Meaning, these lie in the overlapping shaded regions. Here, that is the purple area.
Since the curves in their entirety are not part of the solution set, trim them down to only border the purple region. Now, the solution set of the system is shown.