систима

[Гост]

x.y-y/x=-6
2x/y-3xy=23

[Гост]

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[ammornil]

x.y-y/x=-6
2x/y-3xy=23

[tex]\begin{array}{rlll} & \begin{array}{|l} x\cdot{y}-\frac{\normalsize{y}}{\normalsize{x}}=-6 \\ \frac{\normalsize{2\cdot{x}}}{\normalsize{y}}-3\cdot{x}\cdot{y}=23 \end{array} && \text{ДМ:} x\ne{0}, y\ne{0} \\ \phantom{q} \\ \begin{array}{|l} x\cdot{y}=u \ne 0 \\ \frac{\normalsize{x}}{\normalsize{y}}=v \ne 0 \end{array} \Rightarrow & \begin{array}{|l} u-\frac{\normalsize{1}}{\normalsize{v}}=-6 \\ 2v-3u=23 \end{array} \Leftrightarrow \begin{array}{|l} u=\frac{\normalsize{1}}{\normalsize{v}}-6 \\ 2v-3\left(\frac{\normalsize{1}}{\normalsize{v}}-6 \right)=23 \end{array} \Leftrightarrow \\ \phantom{q} \\ & \Leftrightarrow \begin{array}{|l} u=\frac{\normalsize{1}}{\normalsize{v}}-6 \\ 2v-\frac{\normalsize{3}}{\normalsize{v}}+18=23 \end{array} \Leftrightarrow \begin{array}{|l} u=\frac{\normalsize{1}}{\normalsize{v}}-6 \\ 2v^{2}-5v-3=0 \end{array} \Leftrightarrow \\ \phantom{q} \\ & \Leftrightarrow \begin{array}{|l} u=\frac{\normalsize{1}}{\normalsize{v}}-6 \\ v_{1,2}=\frac{\normalsize{5\pm\sqrt{(-5)^{2}-4\cdot{2}\cdot{(-3)}}}}{\normalsize{2\cdot{2}}} \end{array} \Leftrightarrow \begin{array}{|l} u=\frac{\normalsize{1}}{\normalsize{v}}-6 \\ v_{1,2}=\frac{\normalsize{5\pm7}}{\normalsize{4}} \end{array} \\ \phantom{q} \\ & \Leftrightarrow \begin{array}{lcl} \begin{array}{|l} u_{1}=-\frac{17}{3} \\ v_{1}=3 \end{array} & \cup & \begin{array}{|l} u_{2}=-8 \\ v_{2}=-\frac{1}{2} \end{array} \end{array} \\ \phantom{q} \\ \Rightarrow & \begin{array}{lcl} \begin{array}{|l} x_{1}\cdot{y_{1}}=-\frac{17}{3} \\ \frac{\normalsize{x_{1}}}{\normalsize{y_{1}}}=3 \end{array} & \cup & \begin{array}{|l} x_{2}\cdot{y_{2}}=-8 \\ \frac{\normalsize{x_{2}}}{\normalsize{y_{2}}}=-\frac{1}{2} \end{array} \end{array}
\\ \phantom{q} \\ & \begin{array}{lcl} \begin{array}{|l} x_{1}\cdot{3y_{1}}=-17 \\x_{1}=3y_{1} \end{array} & \cup & \begin{array}{|l} x_{2}\cdot{(-2x_{2})}=-8 \\ y_{2}=-2x_{2} \end{array} \end{array} \\ \phantom{q} \\ & \begin{array}{lcl} \oslash & \cup & \begin{array}{|l} x_{2}^{2}=4 \\ y_{2}=-2x_{2} \end{array} \end{array} \\ \phantom{q} \\ & \begin{array}{lcl} \oslash & \cup & \begin{array}{|l} x_{2}=2 \\ y_{2}=-4 \end{array} \cup \begin{array}{|l} x_{3}=-2 \\ y_{3}=4 \end{array} \end{array} \end{array}[/tex]

[tex][/tex]