Решите систему уравнений:

x+xy^3=9 и xy+xy^2=6

9=x+xy^3 = x * (1+y^3) = x * (1+y) * (1-y + y^2),

6=xy + xy^2 = x*y * (1+y).

Разделим одно уравнение на другое:

9/6 = [ x * (1+y) * (1 - y + y^2) ]/[xy * (1+y) ],

3/2 = (1 - y + y^2) / y;

3y = 2 * (1-y + y^2);

3y = 2 - 2y + 2*y^2;

2*y^2 - 5y + 2 = 0;

D = 5^2 - 4*2*2 = 25 - 16 = 9 = 3^2;

y1 = (5-3) / 4 = 2/4 = 1/2;

y2 = (5+3) / 4 = 8/4 = 2;

x+xy^3 = 9;

x * (1+y^3) = 9;

x = 9 / (1+y^3).

x1 = 9 / (1 + (1/2) ^3) = 9*8 / (8+1) = 8; y1=1/2.

x2 = 9 / (1 + 2^3) = 9/9 = 1; y2 = 2.

Ответ. (8; 1/2), (1; 2).