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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 111 · 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 + 3y = 27 and 3x − 6y = −45 →
  2. 2.2x − 3y = −3 and 6x + y = 61 →
  3. 3.3x + 4y = −17 and 4x + 3y = −25 →
  4. 4.2x + 3y = 1 and 6x + 6y = 0 →
  5. 5.2x + 3y = 35 and 2x + y = 21 →
  6. 6.4x + 3y = −1 and x + 6y = −16 →
  7. 7.7x + 4y = 81 and 4x + 7y = 84 →
  8. 8.3x + 2y = 36 and x − y = −3 →
  9. 9.2x + 4y = 34 and x − 4y = −13 →
  10. 10.5x + 5y = −5 and 6x − 4y = −16 →
  11. 11.x − 2y = −22 and 3x − 3y = −42 →
  12. 12.5x − 2y = 12 and 5x − 6y = −4 →
  13. 13.8x + 7y = 37 and 7x + 8y = 38 →
  14. 14.8x + 5y = −17 and 5x + 8y = −35 →
  15. 15.4x + 9y = 34 and 9x + 4y = −21 →
  16. 16.9x + 5y = 77 and 5x + 9y = 49 →
  17. 17.5x + 4y = 9 and 5x + y = 6 →
  18. 18.9x + 2y = −49 and 2x + 9y = −28 →
  19. 19.5x − 5y = 60 and x − 4y = 39 →
  20. 20.5x + 3y = 14 and 6x − 2y = 56 →
  21. 21.3x + 5y = −37 and 4x + 6y = −48 →
  22. 22.4x + 2y = 16 and 2x + 4y = 20 →
  23. 23.2x + 4y = 22 and 4x + y = −12 →
  24. 24.8x + 6y = 32 and 6x + 8y = 38 →
  25. 25.5x + 3y = −52 and x + 2y = −23 →
  26. 26.3x + 2y = 15 and 3x − 4y = −39 →
  27. 27.9x + 2y = 63 and 2x + 9y = 91 →
  28. 28.3x + 4y = −6 and 4x + 5y = −7 →
  29. 29.4x − 5y = 0 and 5x + y = −29 →
  30. 30.6x + y = −28 and 6x − 5y = −76 →
  31. 31.4x + 8y = −68 and 8x + 4y = −28 →
  32. 32.5x − 2y = 42 and 3x − y = 25 →
  33. 33.2x + 3y = 29 and x + 6y = 55 →
  34. 34.5x − 6y = −34 and 5x + 3y = −43 →
  35. 35.2x + 4y = 6 and 4x + 6y = 4 →
  36. 36.x + 6y = 51 and 6x + y = 26 →
  37. 37.x + y = 8 and x − 3y = 4 →
  38. 38.6x + 4y = 66 and 4x + 6y = 64 →
  39. 39.5x + 9y = 56 and 9x + 5y = 56 →
  40. 40.3x − 2y = −1 and 6x − 3y = −3 →

Answer key

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

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