tex]...

MikoHio @MikoHio

July 2022 1 9 Report

Решите систему уравнений \left \{ {{x-xy=-3} \atop {y+xy=8}} \right. [/tex]

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EBVTJMJMMBZD $x-xy=-3, \ y+xy=8\\
x(1-y)=-3, \ xy=8-y\\
x=- \frac{3}{1-y} = \frac{3}{y-1} , \ x= \frac{8-y}{y} \\
 \frac{3}{y-1} = \frac{8-y}{y} \\
(8-y)(y-1)=3y\\
8y-8-y^2+y-3y=0\\
-y^2+6y-8=0\\
y^2-6y+8=0\\
D=6^2-4*1*8=36-32=4\\
y_1= \frac{6+2}{2} =4\\
y_2= \frac{6-2}{2} =2\\
x_1= \frac{8-4}{4} =1\\
x_2= \frac{8-2}{2} =3\\
Answer: \ (1;4), \ (3;2)$

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