Система

[Гост]

Чрез събиране.....

[Knowledge Greedy]

[tex]\begin{array}{|l} x^2+y^2-2x=3 \\ 2x^2+2y^2-3y=4 \end{array}[/tex]
[tex]\Leftrightarrow[/tex]
[tex]\begin{array}{|l} x^2+y^2-2x=3 \\ 2x-3y=-2 \end{array}[/tex]
[tex]\Leftrightarrow[/tex]
[tex]\begin{array}{|l} x^2+y^2-2x=3 \\ y=\frac{4x+2}{3} \end{array}[/tex]
[tex]\Leftrightarrow[/tex]
[tex]\begin{array}{|l} x^2+\left (\frac{4x+2}{3} \right )^2-2x=3 \\ y=\frac{4x+2}{3} \end{array}[/tex]
[tex]\Leftrightarrow[/tex][tex]\begin{array}{|l} 25x^2-2x-23=0 \\ y=\frac{4x+2}{3} \end{array}[/tex]
[tex]\Leftrightarrow[/tex][tex]\left\{\begin{matrix}
\begin{array}{|l} x_1=1 \\ y=\frac{4x+2}{3} \end{array} \\
\begin{array}{|l} x =- \frac{23}{25} \\ y=\frac{4x+2}{3} \end{array}
\end{matrix}\right.[/tex]
Отговор:
[tex](1;2)[/tex] и [tex]\left ( - \frac{23}{25}; - \frac{14}{25} \right )[/tex]

[Гост]

[tex]\begin{array}{|l} x^2+y^2-2x=3 \\ 2x^2+2y^2-3y=4 \end{array}[/tex]
[tex]\Leftrightarrow[/tex]
[tex]\begin{array}{|l} x^2+y^2-2x=3 \\ 2x-3y=-2 \end{array}[/tex]
[tex]\Leftrightarrow[/tex]
[tex]\begin{array}{|l} x^2+y^2-2x=3 \\ y=\frac{4x+2}{3} \end{array}[/tex]
[tex]\Leftrightarrow[/tex]
[tex]\begin{array}{|l} x^2+\left (\frac{4x+2}{3} \right )^2-2x=3 \\ y=\frac{4x+2}{3} \end{array}[/tex]
[tex]\Leftrightarrow[/tex][tex]\begin{array}{|l} 25x^2-2x-23=0 \\ y=\frac{4x+2}{3} \end{array}[/tex]
[tex]\Leftrightarrow[/tex][tex]\left\{\begin{matrix}
\begin{array}{|l} x_1=1 \\ y=\frac{4x+2}{3} \end{array} \\
\begin{array}{|l} x =- \frac{23}{25} \\ y=\frac{4x+2}{3} \end{array}
\end{matrix}\right.[/tex]
Отговор:
[tex](1;2)[/tex] и [tex]\left ( - \frac{23}{25}; - \frac{14}{25} \right )[/tex]

Благодаря ти сърдечно! #HappyValentinesDay