938 CHAPTER 9 Systems and Matrices Summary Exercises on Systems of Equations This chapter has introduced methods for solving systems of equations, including substitution and elimination, and matrix methods such as the Gauss-Jordan method, the Gaussian elimination method, and Cramer’s rule. Use each method at least once when solving the systems below. Include solutions with nonreal complex number components. For systems with infinitely many solutions, write the solution set using an arbitrary variable. 1. 2x + 5y = 4 3x - 2y = -13 2. x - 3y = 7 -3x + 4y = -1 3. 2x2 + y2 = 5 3x2 + 2y2 = 10 4. 2x - 3y = -2 x + y = -16 3x - 2y + z = 7 5. 6x - y = 5 xy = 4 6. 4x + 2z = -12 x + y - 3z = 13 -3x + y - 2z = 13 7. x + 2y + z = 5 y + 3z = 9 8. x - 4 = 3y x2 + y2 = 8 9. 3x + 6y - 9z = 1 2x + 4y - 6z = 1 3x + 4y + 5z = 0 10. x + 2y + z = 0 x + 2y - z = 6 2x - y = -9 11. x2 + y2 = 4 y = x + 6 12. x + 5y = -23 4y - 3z = -29 2x + 5z = 19 13. y + 1 = x2 + 2x y + 2x = 4 14. 3x + 6z = -3 y - z = 3 2x + 4z = -1 15. 2x + 3y + 4z = 3 -4x + 2y - 6z = 2 4x + 3z = 0 16. 3 x + 4 y = 4 1 x + 2 y = 2 3 17. -5x + 2y + z = 5 -3x - 2y - z = 3 -x + 6y = 1 18. x + 5y + 3z = 9 2x + 9y + 7z = 5 19. 2x2 + y2 = 9 3x - 2y = -6 20. 2x - 4y - 6 = 0 -x + 2y + 3 = 0 21. x + y - z = 0 2y - z = 1 2x + 3y - 4z = -4 22. 2y = 3x - x2 x + 2y = 12 23. 2x - 3y = -2 x + y - 4z = -16 3x - 2y + z = 7 24. x - y + 3z = 3 -2x + 3y - 11z = -4 x - 2y + 8z = 6 25. x2 + 3y2 = 28 y - x = -2 26. 3x - y = -2 y + 5z = -4 -2x + 3y - z = -8 27. 2x2 + 3y2 = 20 x2 + 4y2 = 5 28. x + y + z = -1 2x + 3y + 2z = 3 2x + y + 2z = -7 29. x + 2z = 9 y + z = 1 3x - 2y = 9 30. x2 - y2 = 15 x - 2y = 2 31. -x + y = -1 x + z = 4 6x - 3y + 2z = 10 32. 2x - y - 2z = -1 -x + 2y + 13z = 12 3x + 9z = 6 33. xy = -3 x + y = -2 34. -3x + 2z = 1 4x + y - 2z = -6 x + y + 4z = 3 35. y = x2 + 6x + 9 x + y = 3 36. 5x - 2z = 8 4y + 3z = -9 1 2 x + 2 3 y = -1
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