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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 636 · 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 − y = −16 and x + 5y = 26 →
  2. 2.6x + 4y = −12 and 5x + 3y = −7 →
  3. 3.6x + 4y = −16 and 3x + 6y = 24 →
  4. 4.x + 2y = −1 and 5x + 5y = 15 →
  5. 5.2x − 5y = −16 and 4x + 3y = 20 →
  6. 6.6x − 6y = −30 and x − 4y = −14 →
  7. 7.x + 4y = −16 and x + 5y = −22 →
  8. 8.7x + 3y = −52 and 3x + 7y = −68 →
  9. 9.3x + 5y = 34 and 4x + 2y = 22 →
  10. 10.2x + 6y = 10 and 5x + 4y = 14 →
  11. 11.6x + 5y = 1 and 2x + 4y = −2 →
  12. 12.2x + 5y = 15 and x + 6y = 25 →
  13. 13.2x − 4y = 6 and 5x + 5y = 0 →
  14. 14.7x + 4y = 61 and 4x + 7y = 49 →
  15. 15.x + 4y = 24 and 4x + 4y = 0 →
  16. 16.2x + 3y = −14 and 3x + 2y = −6 →
  17. 17.6x − 6y = −48 and x − 3y = −14 →
  18. 18.8x + 3y = 30 and 3x + 8y = 25 →
  19. 19.5x + 3y = 49 and 4x − 5y = 17 →
  20. 20.x + 6y = 31 and 2x + 6y = 32 →
  21. 21.6x + 5y = −22 and 6x + y = −14 →
  22. 22.x + y = 1 and 2x + y = 10 →
  23. 23.6x − 4y = −30 and 4x − 2y = −14 →
  24. 24.x + 5y = 44 and 4x + 6y = 78 →
  25. 25.6x − 2y = 6 and x + y = −7 →
  26. 26.2x − 2y = −30 and 2x + 5y = 19 →
  27. 27.3x + 3y = 12 and 6x + y = 9 →
  28. 28.6x + 2y = 14 and 6x + 6y = 6 →
  29. 29.x − 6y = 39 and 5x − y = 21 →
  30. 30.7x + 9y = 40 and 9x + 7y = 24 →
  31. 31.6x − y = −11 and 4x − 3y = −19 →
  32. 32.9x + 4y = 104 and 4x + 9y = 104 →
  33. 33.2x + y = −21 and 3x − 4y = −15 →
  34. 34.3x + y = 3 and 3x − 6y = −39 →
  35. 35.5x + 6y = −94 and 5x + y = −49 →
  36. 36.8x + 6y = 46 and 6x + 8y = 24 →
  37. 37.x + 2y = −12 and 2x + y = 3 →
  38. 38.x + 3y = 6 and 5x + 6y = 21 →
  39. 39.5x − 2y = −31 and 6x + y = −10 →
  40. 40.8x + 7y = 64 and 7x + 8y = 71 →

Answer key

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

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