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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 64 · 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. 1.2x + 3y = 16 and 3x + 2y = 14 →
  2. 2.6x + 6y = 42 and 6x − 5y = −57 →
  3. 3.2x − 3y = 4 and 2x + 3y = −32 →
  4. 4.2x + 4y = 6 and 4x + 2y = −12 →
  5. 5.5x + 6y = 59 and 5x + 3y = 47 →
  6. 6.3x − 4y = −33 and 5x + 3y = 32 →
  7. 7.3x + 5y = 16 and 4x − 2y = 4 →
  8. 8.3x + 2y = 41 and 6x + 2y = 68 →
  9. 9.x + 6y = −33 and 5x + 4y = 17 →
  10. 10.x + 2y = 7 and 2x + y = 5 →
  11. 11.6x + 6y = 24 and 6x − 3y = −39 →
  12. 12.4x + 7y = 64 and 7x + 4y = 46 →
  13. 13.4x + 6y = 44 and 2x + 2y = 14 →
  14. 14.2x + 3y = −9 and 3x + 2y = −21 →
  15. 15.6x + 5y = 36 and 4x + 3y = 22 →
  16. 16.2x + y = 23 and x + 2y = 19 →
  17. 17.x + 5y = −17 and 5x − 6y = 70 →
  18. 18.x + 9y = 13 and 9x + y = 37 →
  19. 19.2x + 6y = 32 and 2x + 5y = 28 →
  20. 20.2x + 2y = 10 and 5x + 4y = 22 →
  21. 21.4x − 3y = 5 and 2x − 3y = −5 →
  22. 22.6x + y = 43 and 6x + 2y = 44 →
  23. 23.3x − 5y = 7 and 4x + 6y = 22 →
  24. 24.3x + 4y = 11 and 6x − 3y = 33 →
  25. 25.x + 2y = 11 and 2x − 3y = −6 →
  26. 26.2x + 3y = 3 and 2x + y = −3 →
  27. 27.3x + y = 14 and 5x + y = 20 →
  28. 28.6x + 5y = −11 and 5x + 6y = −22 →
  29. 29.3x + 2y = 28 and x + 6y = 36 →
  30. 30.4x + 2y = 2 and 2x + 4y = 10 →
  31. 31.8x + 2y = 26 and 2x + 8y = 44 →
  32. 32.5x − 2y = 39 and x + 4y = 21 →
  33. 33.3x − 3y = 6 and 2x + 5y = −38 →
  34. 34.7x + 6y = 50 and 6x + 7y = 54 →
  35. 35.3x + 9y = 36 and 9x + 3y = −12 →
  36. 36.5x + 3y = 46 and 5x + 5y = 50 →
  37. 37.2x + 2y = −14 and 2x + 6y = −22 →
  38. 38.3x + 6y = −33 and 6x − 2y = 18 →
  39. 39.x − 2y = −9 and x − 4y = −25 →
  40. 40.4x + 3y = 60 and 3x + 3y = 51 →

Answer key

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

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