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. (y - 2)^2 = x + 4 y = - (1/2)x

Graphing equations involves plotting points on a coordinate system to visually represent the relationship between variables. For the given equations, one is a quadratic equation, which will produce a parabola, while the other is a linear equation, resulting in a straight line. The intersection points of these graphs represent the solutions to the system of equations.

Points of intersection are the coordinates where two graphs meet on the coordinate plane. In the context of a system of equations, these points indicate the values of the variables that satisfy both equations simultaneously. Finding these points is crucial for determining the solution set of the system.

Checking solutions involves substituting the intersection points back into the original equations to verify their validity. This step ensures that the identified solutions are correct and satisfy both equations, confirming that they are indeed the solutions to the system.