Question

2) Решите систему уравнений

Answer 1

$\left \{ {{y+2x=5} \atop {2x-xy=-1}} \right.\\\\\left \{ {{y=5-2x} \atop {2x-x(5-2x)=-1}} \right.\\\\\left \{ {{y=5-2x} \atop {2x-5x+2x^{2}+1=0 }} \right.\\\\\left \{ {{y=5-2x} \atop {2x^{2}-3x+1=0 }} \right.\\\\2x^{2} -3x+1=0\\\\D=(-3)^{2}-4*2*1=9-8=1\\\\x_{1}=\frac{3+1}{4}=1\\\\x_{2}=\frac{3-1}{4}=\frac{1}{2}=0,5\\\\y_{1} =5-2x=5-2*1=3\\\\y_{2}=5-2*0,5=4$

Ответ : (1 ; 3) , ( 0,5 ; 4)