But questions remained—the big three unknowns of who, why, and when.
Sometimes his x has to do duty twice, for different unknowns, in one problem.
He first divides by the factor x -x', reducing it to the degree m - I in both x and x' where m>n; he then forms m equations by equating to zero the coefficients of the various powers of x'; these equations involve the m powers xo, x, - of x, and regarding these as the unknowns of a system of linear equations the resultant is reached in the form of a determinant of order m.
The second class of cases comprises equations involving two unknowns; here we have to deal with two graphs, and the solution of the equation is the determination of their common ordinates.
Simultaneous equations in two unknowns x and y may be treated in the same way, except that each equation gives a functional relation between x and y.
Similarly if we have F more unknowns than we have equations to determine them, we must fix arbitrarily F coordinates before we fix the state of the whole system.
The number F is called the number of degrees of freedom of the system, and is measured by the excess of the number of unknowns over the number of variables.