Question

Розв’язати систему рівнянь

Answer 1

Ответ:

$\bigg (4; \dfrac{1}{3} \bigg ); \quad (3,5; 0,5);$

Объяснение:

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

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

$\displaystyle \Leftrightarrow \left \{ {{(3y-1)(2y-1)=0} \atop {x=5-3y}} \right. \Leftrightarrow \left \{ {{3y-1=0} \atop {x=5-3y}} \right. \vee \left \{ {{2y-1=0} \atop {x=5-3y}} \right. \Leftrightarrow \left \{ {{y=\dfrac{1}{3}} \atop {x=4}} \right. \vee \left \{ {{y=0,5} \atop {x=3,5}} \right. ;$

$\bigg (4; \dfrac{1}{3} \bigg ); \quad (3,5; 0,5);$