Jx + y = 8 Įx + 2y = -7 S5x - y = 21 |2r + 3y = -12 ( x + 3y = 5 \21. 20. |x + y = -3 22. 19. lx - y = 4 |2r – 3y = -8 2 [ 4x + 5y = -3 24. S3x – 6y : |2x + 4y = 3x = 24 = 2 3 25. 23. x + 2y = 0 26. -2y = -8 5x + 4y 3r - Sy = -10 = 1 Зх + Зу 3—1 S2r + y = 1 27. 14x + 2y = 3 2х — у3 0 x - y = 5 1-3x + 3y = 2 28. 30. 8 4х + у 3 29. | 4x + 2y = 12 ( x + 2y = 4 31. Зх — у3 7 32. S 2x – 3y = -1 33. [3x 2y = 0 |2r + 4y = 8 |9х Зу21 34. 5x + 10y = 4 10x + y = 11 1 -x +=y = 1 3 y = -5 -Y- 2r + 3y = 6 x + y = -2 35. 37. 36. 38. 3 X - v = x - 2y = 8. = -1 y = 11 4 1 3 1 = 8 y 4 2x - S 3x – 5y = 3 y = -1 -- - - y 39. 40. l15x + 5y = 21 1 x + 59- 41. 3 = 0 y 42. 3 = 2 2y Hint: Let u = and v = and solve for u and v. Then x = and y = + - -'e + 6112 x - 2y + 3z = 2x + y + z = = 6 2x + y -4 7 X - y 2r \ 45. - 3z = 16 -2y + 4z = - 2z = -11 43. 44. 4 2y + z = 4 3x -3x + 2y - 2z = -10 716 CHAPTER 11 Systems of Equations and Inequalities 2х + у - 32 %3 -2r + 2y + z = -7 3x - 4y - 3z = 7 x - y - z== 1 2x + 3y + z = 2 2r - 3y - z = 0 -x + 2y + z = 5 3x - 4y - z = 1 46. 47. 48. 3x + 2y = 0 2r - 3y - z = 0 3x + 2y + 2z = 2 x + 5y + 3z = 2 2r - 2y + 3z = 6 4х — Зу + 2г - 0 -2r + 3y – 7z = 1 3x - 2y + 2z = 6 7x - 3y + 2z = -1 3y + 4z = y - z = 1 -x + 2y - 3z = -4 3x - 2y - 72 = 0 49. 50. 51. 52. 2r 6 x + y - z = 3x - 2y + z = -5 x + 3y - 2z = 14 x + 2y - z = -3 2x - 4y + z = -7 -2r + 2y - 3z = y + z = -4 x + 4y - 3z = -8 53. 2x - 3y + 4z = -15 5х + у - 2г D 55. 3x - y + 3z = 12 x + y + 6z = 1 54. 56. 12 4

The below figure shows the flow of traffic near a city’s Civic Centre during the rush hours on a typical weekday. Each road can handle a maximum of 1000 cars/ hour without causing congestion. The flow of traffic is controlled by traffic lights at each of the five intersections. a. Formulate a system of linear equations describing the traffic flow.b. Solve the system devised in part (a) ensuring no congestion.c. Suppose 7th avenue between 3rd and 4th streets is soon to be closed for road repairs. Find one possible flow pattern that will result in a smooth flow of traffic.

Solve the following system of equations using the Lower Upper fault without pivoting

4 In the record books of Angorra, the following data was found: x - 2y = 6 Equation 1 -x + 4y = 6 .. Equation 2 Choose the most efficient approaches to solve the system given above. Add the equations. Multiply equation 1 by 2 and subtract the equations. Solve equation 1 for x and substitute the result in equation 2. Substitute -x + 4y for 6 in equation 1.

Consider the following system of equations and its graph: (- 4x + y - 17 3x + 2y 10 18 16 14 12 10 -8 -10 -12 -14- -16 A) What is the soluition of the svstem?