Системи уравнение от 2 степен

[Гост]

[tex]\int_{}^{ } xy-x+y=7
xy+x-y=13

[ammornil]

[tex]\left|x.y-x+y=7 \\ x.y+x-y=13 \right, \hspace{8} \Rightarrow \left| x.y-x+y+(x.y+x-y)=7+13 \\ x.y-x+y-(x.y+x-y)=7-13 \right,\hspace{8} \Rightarrow \left| x.y\cancel{-x}\cancel{+y}+x.y\cancel{+x}\cancel{-y}=20 \\ \cancel{x.y}-x+y\cancel{-x.y}-x+y=-6 \right,\hspace{8} \Rightarrow \\
\left|2.x.y=20 \\ 2.x-2.y=6 \right, \hspace{8} \Rightarrow \left|x.y=10 \\ x-y=3 \right, \hspace{8} \Rightarrow \left|x=3+y \\ (3+y).y=10 \right, \hspace{8} \Rightarrow \left|x=3+y \\ y^2+3.y-10=0 \right, \hspace{8} \Rightarrow \\
\left|x=3+y \\ y_{_{1}}=\frac{-3 -7}{2} \right, \hspace{8} \cup \hspace{8} \left|x=3+y \\ y_{_{2}}=\frac{-3 +7}{2} \right, \\
\left|x_{_{1}}=3-5 \\ y_{_{1}}=-5 \right, \hspace{8} \cup \hspace{8} \left|x_{_{2}}=3+2 \\ y_{_{2}}=2 \right, \\
\left|x_{_{1}}=-2 \\ y_{_{1}}=-5 \right, \hspace{8} \cup \hspace{8} \left|x_{_{2}}=5 \\ y_{_{2}}=2 \right, \\
*** \\
\cyr{OTG}: (-2;-5), (5;2)[/tex]