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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 158 · 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 = 12 and x − 3y = 22 →
  2. 2.5x + 8y = −6 and 8x + 5y = 6 →
  3. 3.3x + 6y = 21 and 3x − 3y = 12 →
  4. 4.2x + 2y = 20 and 4x + 3y = 32 →
  5. 5.3x + 4y = 37 and 5x − 2y = 1 →
  6. 6.5x + 2y = 9 and 3x + 6y = 15 →
  7. 7.2x + 6y = 50 and 6x + 2y = 54 →
  8. 8.6x − 3y = 27 and 5x + 6y = 31 →
  9. 9.4x + 9y = 62 and 9x + 4y = 42 →
  10. 10.5x + y = −11 and 3x + 2y = −8 →
  11. 11.6x + 6y = −30 and 2x − 4y = −16 →
  12. 12.8x + 9y = 66 and 9x + 8y = 70 →
  13. 13.7x + 6y = 2 and 6x + 7y = −2 →
  14. 14.2x + 4y = −24 and 4x + 2y = −30 →
  15. 15.6x + 4y = −82 and 6x − 4y = −26 →
  16. 16.6x + y = −9 and x + 6y = 16 →
  17. 17.6x − 2y = 24 and 6x + 5y = 45 →
  18. 18.x + 6y = 53 and 5x − y = 17 →
  19. 19.4x + 4y = −16 and 3x − 5y = 44 →
  20. 20.3x − 5y = −34 and 3x + 3y = 30 →
  21. 21.4x − 3y = −27 and 3x + y = −4 →
  22. 22.5x + y = 28 and 2x + 2y = 16 →
  23. 23.6x − 4y = −42 and 2x + 6y = 30 →
  24. 24.4x + 4y = 24 and 2x − 2y = −24 →
  25. 25.3x + y = −25 and x − 2y = −13 →
  26. 26.4x + 3y = 60 and 4x − 5y = −4 →
  27. 27.9x + y = 68 and x + 9y = 52 →
  28. 28.x − 5y = 27 and 4x − 5y = 48 →
  29. 29.3x + 4y = 33 and 3x + 6y = 51 →
  30. 30.2x + 2y = 30 and x − 6y = −41 →
  31. 31.2x − 4y = −24 and 6x − 2y = −22 →
  32. 32.x + 6y = 4 and 3x − y = −7 →
  33. 33.4x + 9y = 91 and 9x + 4y = 91 →
  34. 34.8x + 9y = 136 and 9x + 8y = 136 →
  35. 35.6x − 3y = 75 and 3x − 6y = 69 →
  36. 36.x + 5y = 19 and 3x + 4y = 35 →
  37. 37.5x + 5y = 5 and 4x − 2y = −32 →
  38. 38.4x − y = −10 and 3x − 2y = −10 →
  39. 39.2x + 4y = −46 and 6x − 4y = 6 →
  40. 40.5x + y = 39 and 4x + 5y = 69 →

Answer key

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

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