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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 545 · 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. 1.4x + 6y = 24 and x + 4y = 11 →
  2. 2.6x + 2y = 50 and 4x + 5y = 37 →
  3. 3.5x + 6y = 89 and 6x + 5y = 87 →
  4. 4.x + 3y = −15 and 5x − 5y = 45 →
  5. 5.3x + 2y = 7 and 6x − 4y = 46 →
  6. 6.x + 4y = −16 and 4x + y = −34 →
  7. 7.6x + 4y = −14 and 5x + 2y = −21 →
  8. 8.x − y = 11 and 3x + 4y = −30 →
  9. 9.3x + 2y = 19 and 4x − 3y = −3 →
  10. 10.4x + 4y = 0 and 4x − 2y = −18 →
  11. 11.2x + 5y = −22 and 5x + 2y = 29 →
  12. 12.3x + 4y = −40 and 5x − 2y = −32 →
  13. 13.3x + 3y = −6 and 4x + 6y = 0 →
  14. 14.7x + 8y = −25 and 8x + 7y = −20 →
  15. 15.7x + 2y = −11 and 2x + 7y = 29 →
  16. 16.4x + y = 7 and x − 5y = 7 →
  17. 17.x + 4y = −34 and 4x + y = −16 →
  18. 18.3x + 4y = −42 and 6x − 5y = −6 →
  19. 19.2x − 5y = −51 and x + 6y = 51 →
  20. 20.3x + 6y = 54 and 5x + 5y = 55 →
  21. 21.3x + 6y = 51 and 2x − 6y = −36 →
  22. 22.x + 5y = 32 and 5x + y = 16 →
  23. 23.4x + y = 21 and 5x − 2y = 23 →
  24. 24.3x + 5y = 33 and 5x + 3y = 39 →
  25. 25.3x + 6y = −24 and 3x + 3y = −15 →
  26. 26.7x + 3y = −32 and 3x + 7y = −8 →
  27. 27.2x − 6y = 16 and x + 4y = −27 →
  28. 28.6x − 4y = −62 and 3x + 4y = −1 →
  29. 29.2x + 3y = 24 and 3x + 2y = 31 →
  30. 30.6x − 5y = −51 and 3x − 4y = −30 →
  31. 31.2x + 3y = 19 and 3x + 2y = 16 →
  32. 32.2x + 3y = 36 and 6x + y = 60 →
  33. 33.9x + 6y = 93 and 6x + 9y = 87 →
  34. 34.4x − 3y = −44 and 6x − y = −52 →
  35. 35.6x − 2y = 52 and x − 6y = 54 →
  36. 36.4x + 8y = −36 and 8x + 4y = 12 →
  37. 37.x + 3y = −13 and 5x − y = 15 →
  38. 38.3x + 5y = 31 and 5x + 3y = 9 →
  39. 39.6x + 3y = 45 and 6x + 2y = 42 →
  40. 40.x + 5y = 35 and 6x − 4y = 6 →

Answer key

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

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