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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 530 · 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 + 9y = −26 and 9x + y = 6 →
  2. 2.x + 6y = 50 and 2x + 3y = 37 →
  3. 3.9x + 7y = 78 and 7x + 9y = 82 →
  4. 4.3x + 2y = 35 and 2x + 3y = 30 →
  5. 5.6x − y = 22 and x − 6y = −43 →
  6. 6.6x + 4y = 36 and x − 3y = −5 →
  7. 7.3x + y = 29 and 5x − 5y = 35 →
  8. 8.4x + 6y = 14 and x − 2y = −21 →
  9. 9.4x + 3y = 23 and 3x + 4y = 19 →
  10. 10.5x + 6y = −46 and 5x − 3y = 8 →
  11. 11.5x + 8y = 32 and 8x + 5y = 59 →
  12. 12.5x − 3y = 55 and 2x + y = 11 →
  13. 13.2x + 2y = −24 and 4x + y = −27 →
  14. 14.6x + y = −55 and 4x − 2y = −18 →
  15. 15.4x + 6y = 52 and 6x + 4y = 38 →
  16. 16.6x + 2y = 54 and 5x + y = 41 →
  17. 17.x + 4y = 38 and 3x + 4y = 42 →
  18. 18.5x + 2y = −11 and x + y = −7 →
  19. 19.5x + 6y = −5 and 4x − 3y = 35 →
  20. 20.5x + 4y = 48 and 5x − 3y = 34 →
  21. 21.4x + 5y = −77 and x + 6y = −62 →
  22. 22.x − 4y = 12 and 3x − 3y = 18 →
  23. 23.2x + 5y = 29 and 3x − y = −16 →
  24. 24.x − 4y = −23 and x + 6y = 57 →
  25. 25.6x + 9y = 51 and 9x + 6y = 39 →
  26. 26.5x − 5y = 50 and 4x − 2y = 24 →
  27. 27.5x + 6y = 21 and 5x + 4y = 29 →
  28. 28.4x + 6y = 78 and 6x + 4y = 82 →
  29. 29.6x + 5y = −63 and 2x − 6y = 48 →
  30. 30.4x + 3y = 43 and x + 4y = 40 →
  31. 31.5x − 4y = 2 and x − 4y = −6 →
  32. 32.6x − 2y = 14 and 5x + 5y = 25 →
  33. 33.x + 4y = −23 and 2x + 6y = −38 →
  34. 34.2x + 4y = 16 and 4x + 2y = −16 →
  35. 35.x + y = 2 and 6x − y = 61 →
  36. 36.6x + y = 31 and x + 6y = 11 →
  37. 37.x − 6y = −23 and 3x − 4y = 1 →
  38. 38.3x + 4y = −2 and 3x + 5y = −4 →
  39. 39.2x − 5y = 15 and 6x − 3y = 33 →
  40. 40.4x + y = 6 and 4x − 3y = −2 →

Answer key

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

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