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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 16 · 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 + 4y = 2 and 3x + 5y = 9 →
  2. 2.3x + 7y = −34 and 7x + 3y = 14 →
  3. 3.x + 2y = −21 and 2x + y = −24 →
  4. 4.4x + 2y = 46 and 2x + 4y = 50 →
  5. 5.3x − 6y = −57 and 4x − 3y = −51 →
  6. 6.x + 5y = −9 and 2x + 3y = −4 →
  7. 7.8x + 7y = 44 and 7x + 8y = 31 →
  8. 8.4x − 6y = 10 and 3x + 4y = −1 →
  9. 9.9x + 6y = −18 and 6x + 9y = −42 →
  10. 10.2x − 6y = −46 and 5x − 3y = −7 →
  11. 11.2x + 7y = 10 and 7x + 2y = −10 →
  12. 12.2x + 5y = −11 and 5x + 2y = 4 →
  13. 13.2x + 2y = 4 and 4x + 6y = 24 →
  14. 14.6x + 3y = 48 and x − 2y = −7 →
  15. 15.3x + 5y = −14 and 3x − 5y = −4 →
  16. 16.6x + y = −40 and 4x + y = −24 →
  17. 17.4x + 4y = −52 and 5x + y = −37 →
  18. 18.7x + 6y = −1 and 6x + 7y = 1 →
  19. 19.6x + 2y = 4 and 2x + 6y = −4 →
  20. 20.2x + y = 7 and x + 2y = 5 →
  21. 21.2x + 2y = 20 and 3x + y = 14 →
  22. 22.x − 6y = 1 and x + y = −6 →
  23. 23.5x − 5y = −5 and 3x + 4y = −52 →
  24. 24.x − 6y = 37 and 4x + y = −27 →
  25. 25.3x + 3y = −18 and 2x + 6y = −40 →
  26. 26.6x + 5y = −63 and 5x + 4y = −52 →
  27. 27.5x + 8y = 54 and 8x + 5y = 24 →
  28. 28.4x + 9y = 46 and 9x + 4y = 71 →
  29. 29.3x − 4y = −26 and x + 4y = 34 →
  30. 30.3x + y = 5 and x + 3y = −1 →
  31. 31.3x + 2y = 11 and 2x + 3y = 14 →
  32. 32.3x − 6y = 6 and 2x + 6y = 24 →
  33. 33.6x + 3y = −3 and 3x + 2y = −5 →
  34. 34.2x + 2y = 30 and 4x − y = 15 →
  35. 35.7x + 6y = −1 and 6x + 7y = 1 →
  36. 36.3x − y = 11 and 3x + 2y = −13 →
  37. 37.2x + 3y = 14 and 3x + 5y = 23 →
  38. 38.4x + 3y = −54 and 4x + 6y = −72 →
  39. 39.5x + 9y = 49 and 9x + 5y = 77 →
  40. 40.5x + 3y = 34 and 4x + 5y = 48 →

Answer key

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

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