Simultaneous equations which involve the second and higher powers of
the unknown may be impossible of solution. No general rules can be
given, and the solution of any particular problem will largely depend
upon the student's ingenuity. Here we shall only give a few typical
examples.
1. _Equations which may be reduced to linear equations.--Ex._ To solve
x(x - a) = yz, y(y - b) = zx, z(z - c)=xy. Multiply the equations by
y, z and x respectively, and divide the sum by xyz; then
a b c
-- + -- + -- = 0 ... (1).
z x y