Задачи по школьной математике. Простейшие системы уравнений

  1. Найдите x и y, если 2x+11y=-2 и x-3y=-1
  2. Найдите x и y, если 3x-y=2 и 2x+3y=5.
  3. \left\{\begin{array}{l l} \frac{5}{8x-11}=\frac{4}{y},\\5x+11y=54\end{array}\right.
  4. \left\{\begin{array}{l l} (y-4x)^2=4,\\5x+3y=10\end{array}\right.
  5. \left\{\begin{array}{l l} x^3+y-1=0,\\ y^3-4y^2+4y+x^6-1=0\end{array}\right.
  6. \left\{\begin{array}{l l} x^2+y^2=25,\\ y^2-x=5\end{array}\right.
  7. \left\{\begin{array}{l l} 10x-2y+5xy-y^2=0,\\ 3x-13y=11\end{array}\right.
  8. \left\{\begin{array}{l l} 2x^2+x-3=(x-1)(y+5),\\ 2x^2-xy=7+3y\end{array}\right.
  9. \left\{\begin{array}{l l} x^2+2y=-1,\\ y^2+2x=-1\end{array}\right.
  10. \left\{\begin{array}{l l} xy+3y^2-x+4y=7,\\ 2xy+y^2-2x-2y=-1\end{array}\right.
  11. \left\{\begin{array}{l l} x+y=5xy,\\ xy+y=x\end{array}\right.
  12. \left\{\begin{array}{l l} 4x-7y+8z=0,\\ x-2y-z=-3,\\ 6x+2y+3z=-9\end{array}\right.
  13. \left\{\begin{array}{l l} 4x^2+y^2-2xy=7,\\ (2x-y)y=y\end{array}\right.
  14. \left\{\begin{array}{l l} x^2+2y^2-3x-5y=-4,\\ -2x^2-6y^2+2x+15y=6\end{array}\right.
  15. \left\{\begin{array}{l l} x+y=4,\\ x-y=2\end{array}\right.
  16. \left\{\begin{array}{l l} 3x-7y=-1,\\ 4x+3y=11\end{array}\right.
  17. \left\{\begin{array}{l l} 4x+5y=9,\\ 2x-3y=5\end{array}\right.
  18. \left\{\begin{array}{l l} 3x+5y=8,\\ -\displaystyle\frac{3x}{2}+\frac{y}{2}=-1\end{array}\right.
  19. \left\{\begin{array}{l l} y-x=1,\\ \displaystyle\frac{x-y}{3}=1\end{array}\right.
  20. \left\{\begin{array}{l l} 2x+3y=10,\\ 2x-3y=-2\end{array}\right.
  21. \left\{\begin{array}{l l} y+1=2x,\\ \displaystyle\frac{2}{x}=\frac{3}{y+1}\end{array}\right.
  22. \left\{\begin{array}{l l} x+y=4,\\ x-y=2\end{array}\right.
  23. \left\{\begin{array}{l l} 3x+5y=21,\\ 2x-y=1\end{array}\right.
  24. \left\{\begin{array}{l l} 2x-3y=-1,\\ \frac{y}{x}=0,75\end{array}\right.
  25. \left\{\begin{array}{l l} 4x-3y=-4,\\ 4y-10x=3\end{array}\right.
  26. \left\{\begin{array}{l l} \frac{x}{4}-y=-5,\\ \frac{x}{2}-\frac{y}{7}=3\end{array}\right.
  27. \left\{\begin{array}{l l} 3x+2y=5,\\ \frac{5}{3-2x}=\frac{2,5}{1-y}\end{array}\right.
  28. \left\{\begin{array}{l l} \frac{x}{y}=\frac{3}{4},\\ \frac{x-1}{y+2}=\frac{1}{2}\end{array}\right.

Комментариев 4 к “Задачи по школьной математике. Простейшие системы уравнений

  1. 4) (4/17; 50/17), (16/17; 30/17)
    5) (-1;2), (0; 1), (1; 0)
    8) (1; -5/4), (-1/4; -5/4)
    9) (-1;-1)
    10) (-16; 3), (-4; -1)
    11) (0;0), (1/2; 1/3)
    12) (-2; 0; 1)
    13) (корень(7)/2; 0), (-корень(7)/2; 0), (-1;-3), (3/2; 2)
    14) (1; 2), (1; 0,5)

  2. 15) (3; 1)
    16) (2; 1)
    17) (26/11; -1/11)
    18) (1; 1)
    19) нет решений
    20) (2; 2)
    21) (0; -1)

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