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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 560 · 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 + 3y = 5 and 5x + 6y = 22 →
  2. 2.7x + 2y = 34 and 2x + 7y = 29 →
  3. 3.x + 2y = 10 and 2x + y = 17 →
  4. 4.6x + 2y = 46 and 2x + 6y = 26 →
  5. 5.2x − 5y = −11 and 2x − 2y = −2 →
  6. 6.6x + y = −16 and 3x − 6y = −60 →
  7. 7.6x + y = 23 and 5x + 3y = 30 →
  8. 8.5x − y = 34 and 2x + 5y = 46 →
  9. 9.5x − y = −12 and 4x − 2y = −6 →
  10. 10.5x + y = 9 and x + 5y = −3 →
  11. 11.5x + 5y = −60 and 3x + 4y = −42 →
  12. 12.5x + 2y = 30 and 2x + 5y = 33 →
  13. 13.6x + 2y = 54 and 2x − 4y = −10 →
  14. 14.x − 4y = −29 and 6x + y = 51 →
  15. 15.x + 5y = 27 and 4x + y = 13 →
  16. 16.3x + 6y = 9 and 6x + 3y = 27 →
  17. 17.2x − 4y = −38 and x + 4y = 17 →
  18. 18.2x + 3y = 36 and 5x + 4y = 62 →
  19. 19.3x + 2y = 19 and 2x + 3y = 26 →
  20. 20.x + 5y = 18 and 5x + y = 18 →
  21. 21.2x + 4y = 34 and 4x + 2y = 26 →
  22. 22.2x + 8y = 80 and 8x + 2y = 50 →
  23. 23.3x + 4y = 12 and 6x + y = −18 →
  24. 24.7x + 9y = 67 and 9x + 7y = 77 →
  25. 25.3x + 8y = 80 and 8x + 3y = 85 →
  26. 26.5x + 9y = 121 and 9x + 5y = 117 →
  27. 27.4x + y = −9 and x + 6y = 15 →
  28. 28.5x + 6y = 93 and 2x + y = 26 →
  29. 29.6x − y = −30 and 2x + 2y = −24 →
  30. 30.x + 2y = 3 and 5x + 4y = 9 →
  31. 31.x + 3y = 30 and 3x + y = 34 →
  32. 32.x + y = 2 and 5x + 3y = −8 →
  33. 33.5x + y = −16 and 5x + 3y = −8 →
  34. 34.5x + 4y = 49 and x − 4y = 5 →
  35. 35.6x + 5y = 29 and 5x + 6y = 26 →
  36. 36.x + 2y = 20 and 2x + 2y = 28 →
  37. 37.4x + 6y = 30 and 6x − 2y = 34 →
  38. 38.3x + 2y = −3 and 2x + 3y = 8 →
  39. 39.x + 9y = −51 and 9x + y = −59 →
  40. 40.3x + 5y = −43 and x − 3y = 23 →

Answer key

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

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