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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 115 · 40 sums
TalentJR

The trick (Paravartya Yojayet): For ax + by = c and dx + ey = f: bottom = a×e − b×d. x = (c×e − b×f) ÷ bottom; y = (a×f − c×d) ÷ bottom. Special case ax + by = c, bx + ay = f: add the equations to get x + y, subtract to get x − y, then add and halve. Check your x and y in the first equation.

NameDateTime takenScore ___ / 40
  1. 1.4x + 2y = 30 and 2x + 4y = 18 →
  2. 2.3x + 6y = 60 and 3x + 4y = 46 →
  3. 3.x − 5y = −39 and 5x + 5y = −15 →
  4. 4.3x − 4y = 17 and 2x + 6y = −32 →
  5. 5.3x − 3y = −3 and 2x − 6y = 6 →
  6. 6.9x + y = 10 and x + 9y = −70 →
  7. 7.7x + 5y = 46 and 5x + 7y = 50 →
  8. 8.6x + 2y = −24 and 2x + 6y = 40 →
  9. 9.4x + 2y = −12 and 3x − y = −24 →
  10. 10.3x + 2y = 15 and 6x + 6y = 48 →
  11. 11.6x − 6y = −72 and x + 5y = 42 →
  12. 12.4x + 2y = −18 and 4x + 4y = −8 →
  13. 13.x − y = −3 and 6x + y = −60 →
  14. 14.2x − 4y = −28 and 5x − 6y = −34 →
  15. 15.6x + y = −15 and x + 6y = −55 →
  16. 16.4x + 5y = 31 and x − 4y = −8 →
  17. 17.x + 6y = 5 and 6x − 3y = −9 →
  18. 18.x + 6y = 21 and 6x + 2y = 58 →
  19. 19.8x + 7y = −55 and 7x + 8y = −65 →
  20. 20.2x + 7y = −43 and 7x + 2y = 7 →
  21. 21.2x + 5y = 32 and 6x + 6y = 42 →
  22. 22.3x + 4y = 27 and 4x + 3y = 22 →
  23. 23.x + 3y = 12 and 3x − 5y = −6 →
  24. 24.x + 3y = 16 and 5x − 6y = 17 →
  25. 25.9x + 4y = 89 and 4x + 9y = 54 →
  26. 26.8x + 6y = −14 and 6x + 8y = 0 →
  27. 27.6x + y = 62 and x + 6y = 57 →
  28. 28.6x + 6y = 42 and 2x + 6y = 18 →
  29. 29.x + 8y = 15 and 8x + y = −69 →
  30. 30.6x + y = 37 and x + 2y = 19 →
  31. 31.5x − 2y = −16 and 6x + 3y = −30 →
  32. 32.5x + 7y = 14 and 7x + 5y = 34 →
  33. 33.8x + 2y = −2 and 2x + 8y = 52 →
  34. 34.9x + y = 60 and x + 9y = 60 →
  35. 35.5x + 6y = −55 and x − y = 0 →
  36. 36.2x − 3y = 36 and 3x + 6y = −9 →
  37. 37.5x + 9y = −111 and 9x + 5y = −99 →
  38. 38.5x + 9y = −3 and 9x + 5y = 17 →
  39. 39.2x + 2y = −4 and 5x − 6y = −32 →
  40. 40.3x − 6y = 9 and 4x − 2y = 30 →

Answer key

  1. x = 7, y = 1
  2. x = 6, y = 7
  3. x = −9, y = 6
  4. x = −1, y = −5
  5. x = −3, y = −2
  6. x = 2, y = −8
  7. x = 3, y = 5
  8. x = −7, y = 9
  9. x = −6, y = 6
  10. x = −1, y = 9
  11. x = −3, y = 9
  12. x = −7, y = 5
  13. x = −9, y = −6
  14. x = 4, y = 9
  15. x = −1, y = −9
  16. x = 4, y = 3
  17. x = −1, y = 1
  18. x = 9, y = 2
  19. x = 1, y = −9
  20. x = 3, y = −7
  21. x = 1, y = 6
  22. x = 1, y = 6
  23. x = 3, y = 3
  24. x = 7, y = 3
  25. x = 9, y = 2
  26. x = −4, y = 3
  27. x = 9, y = 8
  28. x = 6, y = 1
  29. x = −9, y = 3
  30. x = 5, y = 7
  31. x = −4, y = −2
  32. x = 7, y = −3
  33. x = −2, y = 7
  34. x = 6, y = 6
  35. x = −5, y = −5
  36. x = 9, y = −6
  37. x = −6, y = −9
  38. x = 3, y = −2
  39. x = −4, y = 2
  40. x = 9, y = 3

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