Implicit and explicit equations

In mathematics, an implicit equation is a relation of the form $R (x 1, \dots, x n) = 0$ , where $R$ is a function of several variables. For example, the implicit equation of the unit circle is $x 2 + y 2 - 1 = 0$ . An explicit equation, on the other hand, expresses one variable in terms of one or more others. For example, ${{{1}}}$ is a function that expresses the variable y in terms of x.