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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 762 · 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 + 9y = 68 and 9x + 2y = 75 →
  2. 2.6x + 4y = −18 and 6x − 5y = −99 →
  3. 3.4x − 2y = −14 and 3x + 4y = 17 →
  4. 4.2x + 3y = −7 and x + 3y = −14 →
  5. 5.2x + y = −8 and 3x + y = −14 →
  6. 6.3x − y = 15 and x + 5y = 53 →
  7. 7.4x + 6y = 40 and 6x + 4y = 30 →
  8. 8.x + 6y = −60 and 4x + 5y = −69 →
  9. 9.9x + 6y = 75 and 6x + 9y = 45 →
  10. 10.2x + 6y = 26 and 4x + 2y = 12 →
  11. 11.3x + 8y = −19 and 8x + 3y = −69 →
  12. 12.4x + 3y = 50 and 3x + 4y = 48 →
  13. 13.x + 2y = −1 and 2x + y = −8 →
  14. 14.3x + 2y = 7 and 6x + 3y = 9 →
  15. 15.5x + 7y = 44 and 7x + 5y = 28 →
  16. 16.3x − 2y = −25 and 3x − y = −23 →
  17. 17.2x − 6y = −46 and 5x + 6y = −10 →
  18. 18.9x + 8y = 50 and 8x + 9y = 52 →
  19. 19.x + 3y = 1 and 2x + y = −3 →
  20. 20.3x + y = 6 and 5x − 2y = −1 →
  21. 21.3x − 6y = 12 and 4x − 4y = 24 →
  22. 22.4x + 4y = 12 and 3x + y = 1 →
  23. 23.4x + 7y = 83 and 7x + 4y = 71 →
  24. 24.x + 4y = 17 and 3x + 6y = 33 →
  25. 25.2x + 2y = 0 and 6x + 3y = −9 →
  26. 26.7x + y = 8 and x + 7y = 8 →
  27. 27.2x + y = 3 and x − y = 15 →
  28. 28.5x − 2y = 35 and 2x + 2y = 28 →
  29. 29.6x − y = 34 and x + 3y = 31 →
  30. 30.4x + 6y = 58 and 6x + 4y = 62 →
  31. 31.4x + 6y = −30 and 5x + y = 21 →
  32. 32.6x + 6y = 54 and 2x − y = 0 →
  33. 33.3x + 5y = 42 and 5x + 3y = 54 →
  34. 34.7x + 3y = 55 and 3x + 7y = 75 →
  35. 35.x + 3y = 8 and 5x − 4y = 2 →
  36. 36.x + 4y = 2 and 4x + y = 23 →
  37. 37.7x + 2y = 51 and 2x + 7y = −24 →
  38. 38.2x + 4y = −28 and 4x + 2y = −20 →
  39. 39.2x + 6y = 0 and 5x − 2y = −51 →
  40. 40.5x + 7y = −84 and 7x + 5y = −84 →

Answer key

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

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