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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 729 · 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. 1.3x + 6y = −27 and 5x + 3y = 18 →
  2. 2.6x + y = −62 and 2x + 6y = −66 →
  3. 3.4x − 6y = −60 and 5x − 2y = −53 →
  4. 4.x + 5y = −13 and x − y = −1 →
  5. 5.4x − 5y = 3 and 6x − 4y = 8 →
  6. 6.5x + 5y = 10 and 6x − 2y = 60 →
  7. 7.4x − 5y = −44 and x − y = −9 →
  8. 8.2x + 5y = 34 and 4x + 5y = 38 →
  9. 9.x + y = 4 and 5x − 3y = −4 →
  10. 10.6x − 2y = −38 and 6x + 6y = −30 →
  11. 11.8x + 9y = 6 and 9x + 8y = 11 →
  12. 12.x + 6y = 15 and x − 4y = −15 →
  13. 13.2x + 3y = 9 and 3x + 5y = 14 →
  14. 14.2x + y = 1 and 5x + y = 13 →
  15. 15.8x + 5y = 61 and 5x + 8y = 43 →
  16. 16.7x + 8y = 24 and 8x + 7y = 36 →
  17. 17.6x + 3y = 60 and 3x + 6y = 39 →
  18. 18.x + 2y = 4 and 2x + y = 14 →
  19. 19.9x + 3y = 81 and 3x + 9y = 99 →
  20. 20.3x + 3y = 21 and 4x − 3y = −14 →
  21. 21.4x + 3y = 14 and 3x + y = 18 →
  22. 22.2x + 3y = −16 and 6x + y = 0 →
  23. 23.7x + 2y = 38 and 2x + 7y = −2 →
  24. 24.3x + 4y = −23 and 6x − 5y = 58 →
  25. 25.7x + 2y = 25 and 2x + 7y = 65 →
  26. 26.4x + 3y = 14 and 3x + 5y = 16 →
  27. 27.3x − y = −13 and 6x − 6y = −30 →
  28. 28.4x + 5y = −2 and 5x − 4y = 18 →
  29. 29.4x + 5y = −9 and 5x + 4y = −18 →
  30. 30.5x + y = −39 and 2x + 3y = −39 →
  31. 31.3x + 5y = −72 and 4x − 5y = 9 →
  32. 32.2x + 4y = 32 and 2x − 3y = 4 →
  33. 33.x + y = 12 and x + 2y = 17 →
  34. 34.6x + 3y = −3 and 6x + 4y = −6 →
  35. 35.2x + y = −4 and x + 2y = 10 →
  36. 36.7x + 3y = −44 and 3x + 7y = −36 →
  37. 37.8x + 6y = −14 and 6x + 8y = 14 →
  38. 38.6x + 2y = 30 and 2x + 6y = 58 →
  39. 39.5x + 4y = 11 and 5x + 3y = 12 →
  40. 40.5x + 4y = 7 and 6x + 4y = 10 →

Answer key

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

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