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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 708 · 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. 1.8x + y = 13 and x + 8y = −22 →
  2. 2.6x + 4y = 46 and 6x − 5y = 10 →
  3. 3.x + 4y = 23 and 4x + y = −28 →
  4. 4.4x + 6y = 46 and 6x + 6y = 48 →
  5. 5.x − 3y = 15 and 6x − 4y = 62 →
  6. 6.3x + 8y = 44 and 8x + 3y = −11 →
  7. 7.3x + y = 3 and 6x + 6y = −6 →
  8. 8.5x + 2y = 26 and 2x + 2y = 8 →
  9. 9.2x − 3y = 13 and 2x + y = 9 →
  10. 10.4x + y = −26 and x + 2y = −3 →
  11. 11.x − 4y = 32 and 3x − 6y = 60 →
  12. 12.6x − 6y = −72 and x + 3y = 24 →
  13. 13.5x + 9y = 55 and 9x + 5y = 43 →
  14. 14.4x + 9y = 75 and 9x + 4y = 55 →
  15. 15.5x + y = 48 and 2x + 2y = 24 →
  16. 16.9x + 7y = 44 and 7x + 9y = 52 →
  17. 17.x + 5y = 33 and 6x + y = −5 →
  18. 18.4x + 8y = −16 and 8x + 4y = 40 →
  19. 19.5x + 6y = 49 and 6x + 2y = 38 →
  20. 20.x + 8y = −53 and 8x + y = 17 →
  21. 21.5x + 3y = 48 and x − 6y = 3 →
  22. 22.x + y = −10 and 3x − 6y = 15 →
  23. 23.x + y = 12 and 6x − 4y = 12 →
  24. 24.2x + 9y = 52 and 9x + 2y = 3 →
  25. 25.6x − y = 22 and 2x − 2y = 4 →
  26. 26.6x + y = −3 and 4x + 3y = −23 →
  27. 27.8x + 2y = 32 and 2x + 8y = 38 →
  28. 28.5x − 6y = 59 and 4x + 4y = −32 →
  29. 29.x + 3y = 3 and 4x + 3y = −6 →
  30. 30.x − 6y = −34 and 2x + 3y = 37 →
  31. 31.7x + 3y = 60 and 3x + 7y = 60 →
  32. 32.5x + 6y = 37 and 4x + 3y = 17 →
  33. 33.6x − 2y = 32 and 2x − 2y = 8 →
  34. 34.4x + 6y = 14 and x − 4y = 20 →
  35. 35.x + 2y = −1 and 2x + y = 10 →
  36. 36.4x + 4y = 36 and 3x + 2y = 19 →
  37. 37.3x + y = 16 and 6x − 2y = 4 →
  38. 38.6x + y = −49 and 5x + 4y = −25 →
  39. 39.6x + 5y = −22 and 5x − 2y = 31 →
  40. 40.2x + 5y = 5 and 5x + 5y = −10 →

Answer key

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

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