Решите систему методом введения новых переменных:

Решите задачу:

$\left \{ {{xy+x+y=9,} \atop {x^2y+xy^2=20;}} \right. \left \{ {{xy+(x+y)=9,} \atop {xy(x+y)=20;}} \right. \\ x+y=a, xy=b, \\ \left \{ {{b+a=9,} \atop {ba=20;}} \right. \left \{ {{b=9-a,} \atop {(9-a)a=20;}} \right. \\ -a^2+9a-20=0, \\ a^2-9a+20=0, \\ a_1=4, a_2=5, \\ b_1=5, b_2=4; \\$
$\left [ {{ \left \{ {{x+y=4,} \atop {xy=5;}} \right. } \atop { \left \{ {{x+y=5,} \atop {xy=4;}} \right. }} \right. \left [ {{ \left \{ {{y=4-x,} \atop {x(4-x)=5;}} \right. } \atop { \left \{ {{y=5-x,} \atop {x(5-x)=4;}} \right. }} \right. \\ -x^2+4x-5=0, \\ x^2-4x+5=0, \\ D_1=2^2-5=-1<0, \\ x\in\varnothing; \\ -x^2+5x-4=0, \\ x^2-5x+4=0, \\ x_1=1, x_2=4, \\ y_1=4, y_2=1, \\ (1;4), (4;1).$