§7. Уравнения с двумя перемннными и их системы — 20. Решение систем уравнений с двумя переменными — 384 — стр. 121

\(\left\{\begin{array}{l}x^{2}+y^{2}=9 \\x-y=3\end{array}\right. \Leftrightarrow \left\{\begin{array}{l}(y+3)^{2}+y^{2}=9 \\x=y+3\end{array}\right. \Leftrightarrow \left\{\begin{array}{l}y^{2}+6y+9=9 \\x=y+3\end{array}\right.\Leftrightarrow \\ \Leftrightarrow \left\{\begin{array}{l}2y^{2}+6y=0 \\x=y+3\end{array}\right. \Leftrightarrow \left\{\begin{array}{l}2y(y+3)=0 \\x=y+3\end{array}\right. \Leftrightarrow \\ \Leftrightarrow \left\{\begin{array}{l}y=0 \quad \text{или} \quad y=-3 \\x=y+3\end{array}\right. \Leftrightarrow \left\{\begin{array}{l}\left\{\begin{array}{l}x=0+3=3 \\y=0\end{array}\right. \\\left\{\begin{array}{l}x=-3+3=0 \\y=-3\end{array}\right.\end{array}\right.\).

\(\left\{\begin{array}{l}x-4=4 \\xy=12\end{array}\right. \Leftrightarrow \left\{\begin{array}{l}x=y+4 \\xy=12\end{array}\right. \Leftrightarrow \left\{\begin{array}{l}x=y+4\\(y+4)y=12\end{array}\right.\Leftrightarrow \\ \Leftrightarrow \left\{\begin{array}{l}x=y+4 \\y^{2}+4y-12=0\end{array}\right. \Leftrightarrow \left\{\begin{array}{l}x=y+4 \\(y+6)(y-2)=0\end{array}\right. \Leftrightarrow \\ \Leftrightarrow \left\{\begin{array}{l}x=y+4 \\y=-6 \quad \text{или} \quad y=2\end{array}\right. \Leftrightarrow \left\{\begin{array}{l}\left\{\begin{array}{l}x=-6+4=-2 \\y=-6\end{array}\right. \\\left\{\begin{array}{l}x=2+4=6 \\y=2\end{array}\right.\end{array}\right.\).

\(\left\{\begin{array}{l}2x-y=-1 \\x+y^{2}=10\end{array}\right. \Leftrightarrow \left\{\begin{array}{l}y=2x+1 \\x+(2x+1)^{2}=10\end{array}\right. \Leftrightarrow \left\{\begin{array}{l}y=2x+1\\x+4x^{2}+4x+1=10\end{array}\right.\Leftrightarrow \\ \Leftrightarrow \left\{\begin{array}{l}y=2x+1 \\4x^{2}+5x-9=0\end{array}\right. \Leftrightarrow \left\{\begin{array}{l}y=2x+1 \\(x-1)(4x+9)=0\end{array}\right. \Leftrightarrow \\ \Leftrightarrow \left\{\begin{array}{l}y=2x+1 \\x=1 \quad \text{или} \quad x=-2.25\end{array}\right. \Leftrightarrow \left\{\begin{array}{l}\left\{\begin{array}{l}x=1 \\y=3\end{array}\right. \\\left\{\begin{array}{l}x=-2.25 \\y=-3.5\end{array}\right.\end{array}\right.\).