T. Explain whether a system of two nonlinear equations canhave exactly two solutions. What about exactly three? If not, explain why not. If so, give an example of such a system, ing , and explain why your choice gives two or three anewere. 2. When graphing an inequality explain wh tire- region is the solution?- 3 When you graph a system of inequalities, will there always be a feasible region? If se, explain why. If not, give an example of a graph of inequalities that does not have a feasible region. Why does it not have a feasible- region? 4. If you graph a revenue and cost function, explain how to determine in what regions there is profit. 5. If you perform your break-even analysis and there is more than one solution, explain how you would determine which x-values are profit and which are not. Algebraic For the following exercises, solve the system of nonlinear equations using substitution. 7. 8. Y= - X 9. x2+ 12 = 9For the following exercises, solve the system of nonlinear equations using elimination. 2x3+4y2 = 4 13. "' 294122 = 25x10 For the following exercises, use any method to solve the system of nonlinear equations. yeg- J:2+y= J:+y=2 1E. 17. 9x2 + 25y2 = 225 21. (x-6)2+ y2 = 1 22. 232 - y 23. For the following exercises, use any method to solve the nonlinear system. 24. 25. x2 - yz = 9 x = 3 26 27 * 28. 4x -x- +y=2 29. 2y = -x3x2 - y2 = 12 33. (x-1) +12 = 1 3x 2 2 12 34. 3x2 2 12 35. 82 + 32 16 36. #2+ 42 - 5 x2 + y2-6y = 7 37. x2 + y =1 38. Graphical For the following exercises, graph the inequality. 40. x2 For the following exercises, graph the system of inequalities. Label all points of intersection. 41. x' +y 2x\fTechnology For the following exercises, solve the system of inequalities. Use a calculator to graph the system to confirm the answer. xy Vx 54. "x 2x Real-World Applications For the following exercises, construct a system of nonlinear equations to describe the given behavior, then solve for the requested solutions. 55. Two numbers add up to 300. One number is twice the square of the other number. What are the numbers?- -56. The squares of two numbers add to 960. The second number is half the value of the first number squared. What are the numbers2 57. A laptop company has discovered their cost and revenue functions for each day: C(x) = 3x2-10x + 200 and R(x) = -2x2 + 100x + 50. If they want to make a profit, what is the range of laptops per day that they should produce? Round to the nearest number which would generate profit