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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 734 · 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. 1.5x − 6y = −12 and 6x + 4y = 64 →
  2. 2.2x − y = −9 and 5x + 2y = −27 →
  3. 3.5x + 4y = −26 and 4x + 5y = −28 →
  4. 4.8x + 4y = 16 and 4x + 8y = −4 →
  5. 5.x + y = 7 and 4x + 2y = 30 →
  6. 6.4x − 4y = 0 and 4x + 6y = 60 →
  7. 7.6x + 2y = 12 and 2x + 5y = 43 →
  8. 8.x − 5y = −38 and 5x + 4y = 71 →
  9. 9.3x − 3y = 9 and 6x + y = 25 →
  10. 10.4x + 5y = −13 and 5x + 4y = −5 →
  11. 11.5x + 2y = −27 and 2x + 5y = −15 →
  12. 12.2x − 2y = 16 and 2x + 6y = −8 →
  13. 13.3x + y = 29 and 6x + y = 50 →
  14. 14.4x + 6y = −54 and 4x + y = −29 →
  15. 15.2x + 8y = 6 and 8x + 2y = −66 →
  16. 16.5x + 3y = −18 and 2x + 3y = 9 →
  17. 17.4x + 9y = 34 and 9x + 4y = −21 →
  18. 18.x + 6y = −11 and 4x + 4y = −24 →
  19. 19.5x + 6y = 32 and 6x + 5y = 34 →
  20. 20.6x − 4y = −40 and 2x + y = 3 →
  21. 21.3x − 2y = −16 and x + 2y = 0 →
  22. 22.4x + 7y = −14 and 7x + 4y = 25 →
  23. 23.2x + y = 15 and x + 2y = 15 →
  24. 24.4x + y = 36 and 4x − 4y = 16 →
  25. 25.5x − y = 12 and 4x − y = 9 →
  26. 26.3x + 5y = 26 and 5x − y = 6 →
  27. 27.4x − y = −17 and 4x + y = −15 →
  28. 28.5x − y = −43 and 2x + 5y = −1 →
  29. 29.4x − 3y = 17 and 5x − 2y = 23 →
  30. 30.4x + 2y = 14 and 4x − y = 5 →
  31. 31.x + 8y = 62 and 8x + y = 55 →
  32. 32.3x − 5y = −32 and 2x − 2y = −12 →
  33. 33.5x + 9y = 51 and 9x + 5y = −9 →
  34. 34.3x + 4y = 1 and 3x − y = −34 →
  35. 35.7x + 9y = 119 and 9x + 7y = 121 →
  36. 36.5x + 3y = 2 and 3x + 5y = 14 →
  37. 37.5x + 2y = 27 and x + 2y = 15 →
  38. 38.5x + 6y = 57 and 6x + 5y = 53 →
  39. 39.4x + 3y = 55 and x + 2y = 25 →
  40. 40.4x + y = 13 and 2x − 2y = −16 →

Answer key

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

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