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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 777 · 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. 1.5x + y = 34 and 5x − y = 26 →
  2. 2.5x + 3y = −18 and 2x + 4y = 4 →
  3. 3.3x + 5y = −16 and x + 2y = −5 →
  4. 4.5x + 2y = 50 and 5x + 3y = 55 →
  5. 5.3x − 3y = 30 and 4x − 6y = 58 →
  6. 6.6x − 4y = 38 and 5x + 4y = 61 →
  7. 7.4x − y = 24 and x + 5y = −15 →
  8. 8.6x + 5y = 82 and 4x + 3y = 52 →
  9. 9.4x + 3y = −4 and 2x + 6y = −20 →
  10. 10.2x + 3y = 19 and 3x + 2y = 21 →
  11. 11.x + 5y = 33 and 3x + 5y = 49 →
  12. 12.6x − 3y = −12 and 5x + y = 11 →
  13. 13.2x + 3y = −11 and 5x + 3y = 4 →
  14. 14.x + 5y = −34 and 4x + 6y = −52 →
  15. 15.4x − 2y = 4 and 4x − y = 12 →
  16. 16.2x + 5y = −18 and 3x + y = 12 →
  17. 17.4x + 2y = 0 and 4x − y = −18 →
  18. 18.5x + 4y = 35 and 4x + 5y = 37 →
  19. 19.7x + 3y = 52 and 3x + 7y = 68 →
  20. 20.2x + 3y = 33 and 3x + 6y = 60 →
  21. 21.4x + 5y = −21 and x − 2y = 24 →
  22. 22.6x − 4y = 20 and 2x + 5y = 32 →
  23. 23.5x − 4y = 4 and 3x + 5y = 69 →
  24. 24.3x + 2y = 27 and 4x − 2y = −6 →
  25. 25.6x + 2y = −46 and 6x + 6y = −30 →
  26. 26.6x − 3y = −66 and 6x + 6y = −30 →
  27. 27.5x + 4y = 17 and 4x + 5y = 1 →
  28. 28.2x + 7y = 15 and 7x + 2y = −15 →
  29. 29.6x + y = 37 and x + 6y = −23 →
  30. 30.x + 3y = 24 and 4x + 3y = 42 →
  31. 31.x + 5y = 23 and 5x + y = 19 →
  32. 32.3x + 5y = 67 and 5x − y = 37 →
  33. 33.2x + y = 12 and x + 3y = 16 →
  34. 34.9x + 7y = 68 and 7x + 9y = 60 →
  35. 35.2x − 5y = 31 and 2x + 5y = −19 →
  36. 36.2x + 3y = 32 and x − 2y = −5 →
  37. 37.8x + 7y = 57 and 7x + 8y = 63 →
  38. 38.5x + 2y = −46 and 2x − y = −4 →
  39. 39.3x + 5y = 33 and 3x + y = 21 →
  40. 40.x + 6y = 30 and 4x − 5y = 4 →

Answer key

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

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