Honors Algebra 2: Systems of 3 Linear Equations



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Solve the following systems.

  1. \( 2x + 3y + 6z = 13 \\ 3x + 4y + 2z = 11 \\ x - 3y + 5z = -5\)
  2. Solution (-1, 3, 1)
  3. \( 2x + y - z = -1 \\ -3x + 2y + 2z = 9 \\ x + y - z = 0\)
  4. Solution (-1, 2, 1)
  5. \( 6x + 3y + 2z = 2 \\ -7x -5y + 3z = 22 \\ x + 2y - 5 z= -24\)
  6. Solution (0, -2, 4)
  7. \( 3x + 5y - 7z = -1 \\ -2x + 7y - 3z = -2 \\ x - y + z = -1\)
  8. Solution (-1, -1, -1)
  9. \( 5x + 3y - 2z = 0 \\ 9x + 3y + 10z = 0 \\ 7x - 9y + 3z = 0\)
  10. Solution This is a homogeneous system with the single solution (0, 0, 0)
  11. \( -2x + 4z = 9y + 38 \\ z = 2x - 3y -19 \\ 5x + 3y - 4z -1 = 0\)
  12. Solution (5, -4, 3)
  13. \( 3x - 9y + 7z = -21 \\ -4x + 5y - 2z = 5 \\ -11x + y + 12z = -53\)
  14. Solution (-2, -3, -6)
  15. \( -2x - 8y - 7z = 87 \\ x + 9y - 6z = -2 \\ -10x + 4y - 5z = 5\)
  16. Solution (1, -5, -7)
  17. \( -11x + 3y + 12z = 61 \\ -12x - 11y + 8z = 195 \\ -10x - 6y - 2z = 134\)
  18. Solution (-8, -9, 0)
  19. \( 3x + 4y + 9z = -51 \\ -y - 5z = 24 \\ -11x - 7y - 12z = 55\)
  20. Solution (4, -9, -3)
  21. \( 10x + 3y - z = -55 \\ 3x - 6y - 6z = 36 \\ -6x + 2y - 9z = 106\)
  22. Solution (-6, -1, -8)
  23. \( 4y + 11z = 85 \\ -3x + 6y - 3z = 3 \\ -8x - 9y - 12z = -70\)
  24. Solution (-4, 2, 7)
  25. \( 4x + y - 2z = 0 \\ 2x - 3y + 3z = 9 \\ -6x - 2y + z = 0\)
  26. Solution \( \displaystyle \left( \frac{3}{4}, -2, \frac{1}{2} \right) \)
  27. \( x - y = 2 \\ 3x + z = 11 \\ y - 2z = -3\)
  28. Solution (3, 1, 2)
  29. In a coin bank, there are three times as many dimes as there are nickles and quarters combined. The total value of the 24 coins (all dimes, nickles, and quarters) is $2.90. How many of each kind of coin are there?
  30. Solution 18 dimes, 4 quarters, 2 nickles