In Exercises 63–68, find the solution set for each system by graphing both of the system's equations in the same rectangular coordinate system and finding points of intersection. Check all solutions in both equations. x = (y + 2)^2 - 1 (x - 2)^2 + (y + 2)^2 = 1

Key Concepts

Graphing Equations

Graphing equations involves plotting points on a coordinate system to visualize the relationship between variables. For the given equations, one is a quadratic function and the other represents a circle. Understanding how to graph these shapes accurately is crucial for identifying their points of intersection, which represent the solutions to the system.

Points of Intersection

Points of intersection are the coordinates where two graphs meet on the coordinate plane. In the context of a system of equations, these points represent the solutions that satisfy both equations simultaneously. Finding these points requires solving the equations either algebraically or graphically, and they are essential for determining the solution set.

Checking Solutions

Checking solutions involves substituting the found intersection points back into the original equations to verify their validity. This step ensures that the identified points are indeed solutions to both equations, confirming their accuracy. It is a critical part of the problem-solving process in algebra to ensure that no extraneous solutions have been included.