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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 906 · 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. 1.6x + 4y = 62 and 4x + 4y = 52 →
  2. 2.8x + 7y = 2 and 7x + 8y = 13 →
  3. 3.3x + 5y = 34 and 5x + 3y = 30 →
  4. 4.5x − 4y = 27 and 5x + 5y = 45 →
  5. 5.3x + 5y = 28 and x + 5y = 36 →
  6. 6.2x + y = −6 and 5x + 6y = −43 →
  7. 7.8x + 2y = 56 and 2x + 8y = 44 →
  8. 8.3x + 5y = 46 and 5x − 3y = −14 →
  9. 9.5x + 6y = 54 and 5x − y = 26 →
  10. 10.x + 4y = −13 and 4x + y = 23 →
  11. 11.x + 5y = 28 and 3x + 4y = 40 →
  12. 12.x + 9y = −42 and 9x + y = 22 →
  13. 13.3x − y = −25 and 2x + 2y = −14 →
  14. 14.5x − 3y = 27 and x + y = 15 →
  15. 15.3x + 2y = 5 and x − 4y = 11 →
  16. 16.8x + 2y = 6 and 2x + 8y = −6 →
  17. 17.7x + 6y = 61 and 6x + 7y = 69 →
  18. 18.2x + 3y = 3 and 3x + 2y = −13 →
  19. 19.5x + 5y = 50 and 3x − 6y = 3 →
  20. 20.x + y = 0 and 5x − 3y = −56 →
  21. 21.3x + y = −26 and 5x − 4y = −49 →
  22. 22.7x + 9y = 39 and 9x + 7y = 9 →
  23. 23.5x + 3y = 52 and 3x − 5y = −30 →
  24. 24.5x + 3y = 46 and 3x + 5y = 50 →
  25. 25.3x + y = 2 and 3x + 6y = −3 →
  26. 26.2x + 4y = 22 and 6x + 3y = 48 →
  27. 27.5x + 3y = −7 and 4x + 2y = −6 →
  28. 28.x + y = 6 and 4x + 6y = 32 →
  29. 29.3x − y = −33 and 6x + 6y = 6 →
  30. 30.3x + y = 31 and 5x − 5y = 25 →
  31. 31.8x + 5y = 94 and 5x + 8y = 88 →
  32. 32.6x − 2y = −12 and 5x + 4y = 7 →
  33. 33.2x + 9y = −60 and 9x + 2y = 38 →
  34. 34.5x + 4y = 72 and 2x + 5y = 56 →
  35. 35.2x + 5y = 29 and 6x − y = 39 →
  36. 36.4x + 2y = −24 and 2x + 3y = −8 →
  37. 37.x − 6y = −41 and 2x + 5y = 20 →
  38. 38.6x − 3y = 18 and x + y = 9 →
  39. 39.4x − y = 6 and 3x + y = 8 →
  40. 40.2x − 3y = −10 and 2x + 4y = 18 →

Answer key

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

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