In (1) the unknown is x, and the knowns a, b, c; the coefficients of x^2 and x are a and 2b; the absolute term is c, and the degree is 2. In (2) the unknowns are x and y, and the known a; the degree is 3, i.e. the sum of the indices in the term xy^2. (3) is a homogeneous equation of the second degree in x and y. Equations of the first degree are called _simple_ or _linear_; of the second, _quadratic_; of the third, _cubic_; of the fourth, _biquadratic_; of the fifth, _quintic_, and so on. Of equations containing only one unknown the number of roots equals the degree of the equation; thus a simple equation has one root, a quadratic two, a cubic three, and so on. If one equation be given containing two unknowns, as for example ax + by = c or ax^2 + by^2 = c, it is seen that there are an infinite number of roots, for we can give x, say, any value and then determine the corresponding value of y; such an equation is called _indeterminate_; of the examples chosen the first is a linear and the second a quadratic indeterminate equation. In general, an indeterminate equation results when the number of unknowns exceeds by unity the number of equations. If, on the other hand, we have two equations connecting two unknowns, it is possible to solve the equations separately for one unknown, and then if we equate these values we obtain an equation in one unknown, which is soluble if its degree does not exceed the fourth. By substituting these values the corresponding values of the other unknown are determined. Such equations are called _simultaneous_; and a simultaneous system is a series of equations equal in number to the number of unknowns. Such a system is not always soluble, for it may happen that one equation is implied by the others; when this occurs the system is called _porismatic_ or _poristic_. An _identity_ differs from an equation inasmuch as it cannot be solved, the terms mutually cancelling; for example, the expression x^2 - a^2 = (x - a)(x + a) is an identity, for on reduction it gives 0 = 0. It is usual to employ the sign [Identical to] to express this relation.