Задачи по школьной математике. Системы уравнений

  1. \left\{\begin{array}{l l} x^2-3xy+2y^2=0,\\ x^2+y^2=20 \end{array}\right.
  2. \left\{\begin{array}{l l} x^2+y^2-3xy+4x+4y=-9,\\ xy-3x-3y=7\end{array}\right.
  3. \left\{\begin{array}{l l} y^2+2xy=15,\\ 2x^2+xy=5 \end{array}\right.
  4. \left\{\begin{array}{l l} x^2-2xy+y^2=9,\\ 4x^2+xy+4y^2=18\end{array}\right.
  5. \left\{\begin{array}{l l} \frac{2}{2x-y}+\frac{3}{x-2y}=\frac{1}{2},\\ \frac{2}{2x-y}-\frac{1}{x-2y}=\frac{1}{18} \end{array}\right.
  6. Найдите x+y+4z, если \left\{\begin{array}{l l} 2x+3y+2z=13,\\ 3x+5y=-7\end{array}\right..
  7. \left\{\begin{array}{l l} xy(x-y)=-20,\\ \frac{1}{x}-\frac{1}{y}=\frac{5}{4} \end{array}\right.

Ответы

  1.  (\sqrt{10};\sqrt{10}), (-\sqrt{10}; -\sqrt{10})
  2. (-1; -1)
  3. (1; 3), (-1;-3)
  4. (2;-1), (-1;2), (-2;1), (1;-2)
  5. (5; -2)
  6. 33
  7. (1; -4), (4;-1),  (\frac{-5+\sqrt{41}}{2};\frac{5+\sqrt{41}}{2}), (\frac{-5-\sqrt{41}}{2};\frac{5-\sqrt{41}}{2})