1ºBACH CCSS SISTEMAS DE ECUACIONES NO LINEALES (ACTIVIDADES)

Sistemas de ecuaciones no lineales

Actividades

1. \(\left\{\begin{array}{l} x^2+y^2=13 \\ 3x-2y=0 \end{array}\right.\)
2. \(\left\{\begin{array}{l} x^2+y^2=10 \\ x^2-y^2=8 \end{array}\right.\)
3. \(\left\{\begin{array}{l} x^2-2xy+y^2=16 \\ x+y=6 \end{array}\right.\)
4. \(\left\{\begin{array}{l} x^2+y^2=25 \\ xy=12 \end{array}\right.\)
5. \(\left\{\begin{array}{l} x^2-y=0 \\ x-y=0 \end{array}\right.\)
6. \(\left\{\begin{array}{l} y=x^2+4x+2 \\ x+y+2=0 \end{array}\right.\)
7. \(\left\{\begin{array}{l} y=x^2+4x+2 \\ 4x-y+2=0 \end{array}\right.\)
8. \(\left\{\begin{array}{l} y=x^2+4x+2 \\ x-y+2=0 \end{array}\right.\)
9. \(\left\{\begin{array}{l} x+2y=0 \\ x^2+y^2=5 \end{array}\right.\)
10. \(\left\{\begin{array}{l} 2x-y=3 \\ x^2-y^2=3 \end{array}\right.\)
11. \(\left\{\begin{array}{l} 3x^2+5y^2=20 \\ 4x^2-y^2=-4 \end{array}\right.\)
12. \(\left\{\begin{array}{l} x^2-2(x-y)=35 \\ -x+y=5 \end{array}\right.\)
13. \(\left\{\begin{array}{l} xy=15 \\ \displaystyle{\frac{x}{y}}=\displaystyle{\frac{5}{3}} \end{array}\right.\)
14. \(\left\{\begin{array}{l} 2x-y=-1 \\ (x-1)^2+y=3 \end{array}\right.\)
15. \(\left\{\begin{array}{l} x^2-y^2=8 \\ xy=-3 \end{array}\right.\)
16. \(\left\{\begin{array}{l} x^2+y^2-4x-6y+11=0 \\ x^2+y^2-6x-8y+21=0 \end{array}\right.\)
17. \(\left\{\begin{array}{l} 2x^2-10y^2=8 \\ x^2-3y^2=6 \end{array}\right.\)
18. \(\left\{\begin{array}{l} x^2=18-y^2 \\ x=-y \end{array}\right.\)
19. \(\left\{\begin{array}{l} x^2+xy=77 \\ xy + y^2=44 \end{array}\right.\)
20. \(\left\{\begin{array}{l} x^2+y^2=25 \\ x-\displaystyle{\frac{3}{4}}y=0 \end{array}\right.\)
21. \(\left\{\begin{array}{l} \displaystyle{\frac{1}{x}}+\displaystyle{\frac{1}{y}}=\displaystyle{\frac{5}{6}} \\ xy =6 \end{array}\right.\)
22. \(\left\{\begin{array}{l} x^2+y^2=61 \\ xy=30 \end{array}\right.\)
23. \(\left\{\begin{array}{l} x^2+y^2=25 \\ xy+12=0 \end{array}\right.\)
24. \(\left\{\begin{array}{l} x^2-xy+y^2=7 \\ x+y=5 \end{array}\right.\)
25. \(\left\{\begin{array}{l} 2x^2-5y^2=13 \\ xy+3=0 \end{array}\right.\)
26. \(\left\{\begin{array}{l} y=1+2x \\ x^2+y^2+6x=16 \end{array}\right.\)
27. \(\left\{\begin{array}{l} x^2+xy+y^2=19 \\ xy=6 \end{array}\right.\)
28. \(\left\{\begin{array}{l} xy=8 \\ x+y=6 \end{array}\right.\)
29. \(\left\{\begin{array}{l} x+y=6 \\ xy=9 \end{array}\right.\)
30. \(\left\{\begin{array}{l} 2x^2-y^2=-1 \\ x^2+2y^2=22 \end{array}\right.\)
31. \(\left\{\begin{array}{l} x^2+y^2+9x+14=0 \\ y^2=16+4x \end{array}\right.\)
32. \(\left\{\begin{array}{l} x+y=3 \\ \displaystyle{\frac{1}{x}}+\displaystyle{\frac{1}{y}}=\displaystyle{\frac{3}{2}} \end{array}\right.\)
33. \(\left\{\begin{array}{l} \displaystyle{\frac{1}{x}}+\displaystyle{\frac{1}{y}}=\displaystyle{\frac{5}{6}} \\ \displaystyle{\frac{1}{x}}-\displaystyle{\frac{1}{y}}=\displaystyle{\frac{1}{6}} \end{array}\right.\)
34. \(\left\{\begin{array}{l} \displaystyle{\frac{2}{x}}+\displaystyle{\frac{3}{y}}=\displaystyle{\frac{17}{12}} \\ \displaystyle{\frac{1}{x}}-\displaystyle{\frac{2}{y}}=-\displaystyle{\frac{1}{6}} \end{array}\right.\)
35. \(\left\{\begin{array}{l} y=-x^2+4x+1 \\ x+y=5 \end{array}\right.\)
36. \(\left\{\begin{array}{l} x-3y=-5 \\ xy-2x-y=1 \end{array}\right.\)
37. \(\left\{\begin{array}{l} (x+y)(x-y)=7 \\ 3x-4y=0 \end{array}\right.\)
38. \(\left\{\begin{array}{l} xy=4 \\ x^2+y^2=17 \end{array}\right.\)
39. \(\left\{\begin{array}{l} xy=15 \\ \displaystyle{\frac{x}{y}}=\displaystyle{\frac{5}{3}} \end{array}\right.\)
40. \(\left\{\begin{array}{l} x-y+3=0 \\ x^2+y^2=5 \end{array}\right.\)
41. \(\left\{\begin{array}{l} x^2+y^2-5x-5y+10=0 \\ x^2-y^2-5x+5y+2=0 \end{array}\right.\)
42. \(\left\{\begin{array}{l} 4x^2-y^2=0 \\ 4x^2+3y^2=64 \end{array}\right.\)
43. \(\left\{\begin{array}{l} x-y=15 \\ xy=100 \end{array}\right.\)
44. \(\left\{\begin{array}{l} y=\displaystyle{\sqrt[]{x+1}} \\ y=5-x \end{array}\right.\)
45. \(\left\{\begin{array}{l} x^2-y^2=3 \\ x^2+y^2=5 \end{array}\right.\)
46. \(\left\{\begin{array}{l} x+7=y^2 \\ \displaystyle{\frac{1}{x}}+\displaystyle{\frac{1}{y}}=\displaystyle{\frac{5}{xy}} \end{array}\right.\)

Soluciones:

1. \(x_1=2,y_1=3;x_2=-2,y_2=-3\)
2. \(x_1=-3,y_1=-1;x_2=3,y_2=-1;x_3=-3,y_3=1;x_4=3,y_4=1\)
3. \(x_1=1,y_1=5;x_2=5,y_2=1\)
4. \(x_1=-3,y_1=-4;x_2=3,y_2=4;x_3=-4,y_3=-3;x_4=4,y_4=3\)
5. \(x_1=0,y_1=0;x_2=1,y_2=1\)
6. \(x_1=-4,y_1=2;x_2=-1,y_2=-1\)
7. \(x_1=0,y_1=2\)
8. \(x_1=0,y_1=2;x_2=-3,y_2=-1\)
9. \(x_1=2,y_1=-1;x_2=-2,y_2=1\)
10. \(x_1=2,y_1=1\)
11. \(x_1=0,y_1=-2;x_2=0,y_2=2\)
12. \(x_1=-5,y_1=0;x_2=5,y_2=10\)
13. \(x_1=-5,y_1=-3;x_2=5,y_2=3\)
14. \(x_1=-1,y_1=-1;x_2=1,y_2=3\)
15. \(x_1=-3,y_1=1;x_2=3,y_2=-1\)
16. \(x_1=3,y_1=2;x_2=1,y_2=4\)
17. \(x_1=-3,y_1=-1;x_2=3,y_2=-1;x_3=-3,y_3=1;x_4=3,y_4=1\)
18. \(x_1=-3,y_1=3;x_2=3,y_2=-3\)
19. \(x_1=-7,y_1=-4;x_2=7,y_2=4\)
20. \(x_1=-3,y_1=-4;x_2=3,y_2=4\)
21. \(x_1=2,y_1=3;x_2=3,y_2=2\)
22. \(x_1=-5,y_1=-6;x_2=5,y_2=6;x_3=-6,y_3=-5;x_4=6,y_4=5\)
23. \(x_1=-3,y_1=4;x_2=3,y_2=-4;x_3=-4,y_3=3;x_4=4,y_4=-3\)
24. \(x_1=3,y_1=2;x_2=2,y_2=3\)
25. \(x_1=-3,y_1=1;x_2=3,y_2=-1\)
26. \(x_1=-3,y_1=-5;x_2=1,y_2=3\)
27. \(x_1=-2,y_1=-3;x_2=2,y_2=3;x_3=-3,y_3=-2;x_4=3,y_4=2\)
28. \(x_1=4,y_1=2;x_2=2,y_2=4\)
29. \(x_1=3,y_1=3\)
30. \(x_1=-2,y_1=-3;x_2=2,y_2=-3;x_3=-2,y_3=3;x_4=2,y_4=3\)
31. \(x_1=-3,y_1=-2;x_2=-3,y_2=2\)
32. \(x_1=2,y_1=1;x_2=1,y_2=2\)
33. \(x_1=2,y_1=3\)
34. \(x_1=3,y_1=4\)
35. \(x_1=2,y_1=4;x_2=4,y_2=1\)
36. \(x_1=-2,y_1=1;x_2=4,y_2=3\)
37. \(x_1=-4,y_1=-3;x_2=4,y_2=3\)
38. \(x_1=-1,y_1=-4;x_2=1,y_2=4;x_3=-4,y_3=-1;x_4=4,y_4=1\)
39. \(x_1=-5,y_1=-3;x_2=5,y_2=3\)
40. \(x_1=-2,y_1=1;x_2=-1,y_2=2\)
41. \(x_1=2,y_1=1;x_2=2,y_2=4;x_3=3,y_3=1;x_4=3,y_4=4\)
42. \(x_1=-2,y_1=-4;x_2=2,y_2=-4;x_3=-2,y_3=4;x_4=2,y_4=4\)
43. \(x_1=-5,y_1=-20;x_2=20,y_2=5\)
44. \(x_1=3,y_1=2\)
45. \(x_1=-2,y_1=-1;x_2=2,y_2=-1;x_3=-2,y_3=1;x_4=2,y_4=1\)
46. \(x_1=9,y_1=-4;x_2=2,y_2=3\)