To determine whether an equation allows you to find the x- and y-coordinates of any point on the xy-plane, we need to consider what an equation represents and how it can be used in a coordinate system.
An equation involving two variables, typically x and y, represents a set of points on the Cartesian plane that satisfy the given relation. However, not every possible point (x, y) on the Cartesian plane will necessarily satisfy any given equation.
For example, consider the equation of a line, such as [tex]\(y = 2x + 3\)[/tex]. This equation defines a specific line on the plane, and only the points on this line will satisfy the equation. Similarly, for a circle given by [tex]\(x^2 + y^2 = r^2\)[/tex], only the points on that circle will satisfy the equation.
Therefore, it is not true that an equation allows you to find the x- and y-coordinates of any point on the xy-plane because the equation will only describe a specific set of points that satisfy it.
With this understanding, we conclude that the statement "An equation allows you to find the x- and y-coordinates of any point on the xy-plane" is:
B. False
