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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 732 · 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. 1.3x + 9y = −42 and 9x + 3y = −54 →
  2. 2.x − 6y = −12 and 4x − 3y = −27 →
  3. 3.6x + 4y = 78 and 3x + 4y = 51 →
  4. 4.x + 4y = −1 and x + 5y = 1 →
  5. 5.4x + 3y = 45 and 3x + 4y = 46 →
  6. 6.x + 4y = 30 and 3x + 2y = 20 →
  7. 7.3x + 2y = −9 and 3x + y = −12 →
  8. 8.5x + 4y = 77 and 5x + 6y = 93 →
  9. 9.3x + 7y = 11 and 7x + 3y = 39 →
  10. 10.2x + 6y = −16 and 3x − y = −14 →
  11. 11.x − 6y = 49 and 3x + 2y = 7 →
  12. 12.7x + 2y = −11 and 2x + 7y = 29 →
  13. 13.4x + 3y = 10 and 3x + 4y = 11 →
  14. 14.x − 5y = 25 and 5x + 2y = −37 →
  15. 15.x + 3y = −3 and 6x + 2y = −34 →
  16. 16.x + 3y = −29 and 3x + y = −31 →
  17. 17.x − 5y = 22 and 3x − y = −4 →
  18. 18.9x + 3y = 45 and 3x + 9y = −9 →
  19. 19.2x + 6y = 14 and 3x + 2y = 14 →
  20. 20.x − 6y = −21 and 5x − 4y = −1 →
  21. 21.4x + 3y = −18 and 3x + y = −16 →
  22. 22.8x + 2y = 60 and 2x + 8y = 30 →
  23. 23.x + 4y = 9 and 4x + y = −9 →
  24. 24.2x + 5y = 17 and 5x + 4y = 34 →
  25. 25.5x + y = 22 and x + 5y = −10 →
  26. 26.5x + 3y = 60 and 3x + 2y = 37 →
  27. 27.3x + 6y = −6 and 4x − 5y = 18 →
  28. 28.4x + 5y = −21 and 5x + 4y = −6 →
  29. 29.7x + 5y = 94 and 5x + 7y = 98 →
  30. 30.3x + 5y = 48 and 6x + 4y = 60 →
  31. 31.9x + 5y = 54 and 5x + 9y = 86 →
  32. 32.4x − 2y = 24 and 5x − 4y = 27 →
  33. 33.4x + 3y = −1 and 2x + 4y = −8 →
  34. 34.x + 4y = 12 and x − y = −13 →
  35. 35.4x − 4y = −16 and 4x − 3y = −14 →
  36. 36.2x + y = 7 and x + 2y = 11 →
  37. 37.x + y = −6 and 3x + y = −14 →
  38. 38.x + 5y = −25 and 6x − y = 36 →
  39. 39.6x − 4y = 72 and 4x + 2y = 6 →
  40. 40.2x + 5y = 27 and 6x + y = 11 →

Answer key

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

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