Solutions for Systems of Nonlinear Equations and Inequalities: Two Variables
Solutions to Try Its
1. (−21,21) and (2,8)
2. (−1,3)
3. {(1,3),(1,−3),(−1,3),(−1,−3)}
4. Shade the area bounded by the two curves, above the quadratic and below the line.
Solutions to Odd-Numbered Exercises
1. A nonlinear system could be representative of two circles that overlap and intersect in two locations, hence two solutions. A nonlinear system could be representative of a parabola and a circle, where the vertex of the parabola meets the circle and the branches also intersect the circle, hence three solutions.
3. No. There does not need to be a feasible region. Consider a system that is bounded by two parallel lines. One inequality represents the region above the upper line; the other represents the region below the lower line. In this case, no points in the plane are located in both regions; hence there is no feasible region.
5. Choose any number between each solution and plug into C(x) and R(x). If C(x)<R(x), then there is profit.
7. (0,−3),(3,0)
9. (−232,232),(232,−232)
11. (−3,0),(3,0)
13. (41,−862),(41,862)
15. (−4398,4199),(4398,4199)
17. (0,2),(1,3)
19. (−21(5−1),21(1−5)),(21(5−1),21(1−5))
21. (5,0)
23. (0,0)
25. (3,0)
27. No Solutions Exist
29. No Solutions Exist
31. (−22,−22),(−22,22),(22,−22),(22,22)
33. (2,0)
35. (−7,−3),(−7,3),(7,−3),(7,3)
37. (−21(73−5),21(7−73)),(21(73−5),21(7−73))
39.
41.
43.
45.
47.
49. (−238370,−22935),(−238370,22935),(238370,−22935),(238370,22935)
51. No Solution Exists
53. x=0,y>0 and 0<x<1,x<y<x1
55. 12, 288
57. 2–20 computers