Either one of the given two formulas requires two values in order to calculate the third and so are two dimensional but we can use the two equations to solve for one variable. x+ y= 3 is the equation of a plane in three dimensions. is a cone (In cylindrical coordinates it reduces to , two lines at 45 degrees to the xy-plane- think of that rotated around the z-axis). If then so that [itex]x^2- y^= x^2- (3- x)^2= x^2- 9+ 6x- x^2= 9+ 6x= z^2[/itex]. If we let z= t then and . Since x, y, and z can be written in terms of a single variable, it is, by definition of "dimension", one- dimensional.
(The first formula, x+y= 3, has only two variables but that only means that z can be anything. Some points on that plane are (1, 2, 0), (1, 2, 0.5), (0, 3, 20), etc.)