Question

Решите систему уравнений
{х+3у=5, {4у+ху=6

Answer 1

$\displaystyle \left \{ {{x+3y=5~} \atop {4y+xy=6}} \right. \ \ \ \Leftrightarrow\ \ \ \left \{ {{x=5-3y~~} \atop {y(4+x)=6}} \right.\\\\\\\left \{ {{x=5-3y~~~~~~~~} \atop {y(4+5-3y)=6}} \right. \ \ \ \Leftrightarrow\ \ \ \left \{ {{x=5-3y~~~~~~~~~~~~~~~} \atop {9y-3y^2=6}~~~|:(-3) \right.\\\\\\\left \{ {{x=5-3y~~~~~~} \atop {y^2-3y+2=0} \right.\ \ \ \Leftrightarrow\ \ \ \left \{ {{x=5-3y~~~~~~~} \atop {(y-2)(y-1)=0} \right.$

$\displaystyle\left [ {{y_1=2; ~~x_1=5-3\cdot 2=-1} \atop {y_2=1;~~x_2=5-3\cdot 1=2~~}} \right.$

Ответ : (-1; 2) ,  (2; 1)