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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 506 · 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.x + 2y = 9 and 2x + y = 3 →
  2. 2.4x + 3y = 5 and 2x + 2y = 2 →
  3. 3.x + 3y = 8 and 3x + y = −16 →
  4. 4.5x + 2y = −39 and 2x + 5y = −24 →
  5. 5.6x + 5y = 34 and 3x + y = 14 →
  6. 6.x + 6y = 34 and 6x − 3y = −69 →
  7. 7.3x − 3y = −21 and x + y = 9 →
  8. 8.6x + 5y = 48 and 4x + 6y = 48 →
  9. 9.x − 6y = 33 and 3x + 6y = −21 →
  10. 10.3x − 3y = 21 and 3x + 2y = 16 →
  11. 11.3x + 3y = 3 and 5x − 6y = −39 →
  12. 12.8x + 5y = 82 and 5x + 8y = 61 →
  13. 13.2x + 6y = 40 and 2x + y = −5 →
  14. 14.9x + 4y = −59 and 4x + 9y = −84 →
  15. 15.2x + 3y = 1 and x + 6y = 5 →
  16. 16.4x + 6y = −6 and 6x + 4y = 6 →
  17. 17.2x + 5y = 43 and 3x − y = 5 →
  18. 18.4x − 3y = 11 and 5x − 6y = 7 →
  19. 19.3x + 2y = −9 and x + 4y = −33 →
  20. 20.9x + 5y = 108 and 5x + 9y = 116 →
  21. 21.9x + y = 68 and x + 9y = 52 →
  22. 22.6x + y = 57 and 4x − y = 23 →
  23. 23.x − y = −5 and 2x + y = 17 →
  24. 24.7x + 6y = 39 and 6x + 7y = 39 →
  25. 25.2x + 7y = 4 and 7x + 2y = 59 →
  26. 26.3x + 8y = 81 and 8x + 3y = 51 →
  27. 27.x + 5y = −19 and 5x + 3y = −51 →
  28. 28.2x − 6y = 36 and 5x + 2y = 5 →
  29. 29.6x + 3y = 15 and 4x − 6y = 2 →
  30. 30.9x + 5y = −78 and 5x + 9y = −62 →
  31. 31.3x + 5y = 59 and 2x − y = 9 →
  32. 32.4x + 8y = 52 and 8x + 4y = 8 →
  33. 33.3x + 4y = 27 and 4x + 3y = 29 →
  34. 34.2x + 9y = 89 and 9x + 2y = 54 →
  35. 35.x + 5y = −14 and x + 3y = −10 →
  36. 36.3x + 3y = 3 and 4x + y = −5 →
  37. 37.2x + 2y = 14 and 2x + y = 9 →
  38. 38.3x + 5y = −22 and 5x + 3y = −10 →
  39. 39.x + 4y = 39 and 2x + 5y = 54 →
  40. 40.5x + 2y = −3 and x − 2y = 21 →

Answer key

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

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