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.
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.