901 9.2 Matrix Solution of Linear Systems Use the Gauss-Jordan method to solve each system of equations. For systems in two variables with infinitely many solutions, write the solution with y arbitrary. For systems in three variables with infinitely many solutions, write the solution set with z arbitrary. See Examples 1–4. 21. x + y = 5 x - y = -1 22. x + 2y = 5 2x + y = -2 23. 3x + 2y = -9 2x - 5y = -6 24. 2x - 5y = 10 3x + y = 15 25. 6x - 3y - 4 = 0 3x + 6y - 7 = 0 26. 2x - 3y - 10 = 0 2x + 2y - 5 = 0 27. 2x - y = 6 4x - 2y = 0 28. 3x - 2y = 1 6x - 4y = -1 29. 3 8 x - 1 2 y = 7 8 -6x + 8y = -14 30. 1 2 x + 3 5 y = 1 4 10x + 12y = 5 31. x + y - 5z = -18 3x - 3y + z = 6 x + 3y - 2z = -13 32. -x + 2y + 6z = 2 3x + 2y + 6z = 6 x + 4y - 3z = 1 33. x + y - z = 6 2x - y + z = -9 x - 2y + 3z = 1 34. x + 3y - 6z = 7 2x - y + z = 1 x + 2y + 2z = -1 35. x - z = -3 y + z = 9 x + z = 7 36. -x + y = -1 y - z = 6 x + z = -1 37. y = -2x - 2z + 1 x = -2y - z + 2 z = x - y 38. x = -y + 1 z = 2x y = -2z - 2 39. 2x - y + 3z = 0 x + 2y - z = 5 2y + z = 1 40. 4x + 2y - 3z = 6 x - 4y + z = -4 -x + 2z = 2 41. 3x + 5y - z + 2 = 0 4x - y + 2z - 1 = 0 -6x - 10y + 2z = 0 42. 3x + y + 3z - 1 = 0 x + 2y - z - 2 = 0 2x - y + 4z - 4 = 0 43. x - 8y + z = 4 3x - y + 2z = -1 44. 5x - 3y + z = 1 2x + y - z = 4 45. x - y + 2z + w = 4 y + z = 3 z - w = 2 x - y = 0 46. x + 2y + z - 3w = 7 y + z = 0 x - w = 4 -x + y = -3 47. x + 3y - 2z - w = 9 4x + y + z + 2w = 2 -3x - y + z - w = -5 x - y - 3z - 2w = 2 48. 2x + y - z + 3w = 0 3x - 2y + z - 4w = -24 x + y - z + w = 2 x - y + 2z - 5w = -16
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