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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 108 · 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 = 46 and 4x + 2y = 32 →
  2. 2.x + 4y = 7 and x + 6y = 11 →
  3. 3.6x + 7y = 34 and 7x + 6y = 31 →
  4. 4.7x + 5y = 9 and 5x + 7y = 27 →
  5. 5.5x + 3y = −14 and 5x + 5y = −10 →
  6. 6.2x + 6y = −42 and 2x + 4y = −30 →
  7. 7.6x + 3y = −12 and 4x − 6y = −24 →
  8. 8.9x + 3y = 63 and 3x + 9y = −3 →
  9. 9.9x + 6y = 21 and 6x + 9y = 9 →
  10. 10.7x + 4y = −12 and 4x + 7y = 12 →
  11. 11.5x + 7y = −36 and 7x + 5y = −12 →
  12. 12.5x + y = 47 and x + 5y = 19 →
  13. 13.5x + 7y = 83 and 7x + 5y = 73 →
  14. 14.6x + 2y = −4 and 2x + 6y = −28 →
  15. 15.6x + 5y = 9 and 2x + y = 5 →
  16. 16.5x − y = −13 and 2x − 3y = 13 →
  17. 17.5x − 5y = 65 and 6x + 6y = −6 →
  18. 18.4x + 6y = 2 and 5x − 5y = 15 →
  19. 19.6x + 2y = −44 and 3x − 4y = −47 →
  20. 20.5x + 2y = −3 and x + y = 3 →
  21. 21.x + 8y = −73 and 8x + y = −17 →
  22. 22.8x + 2y = 86 and 2x + 8y = 74 →
  23. 23.2x + 4y = 34 and 3x − 5y = 7 →
  24. 24.8x + 5y = 54 and 5x + 8y = 63 →
  25. 25.7x + 2y = 55 and 2x + 7y = −10 →
  26. 26.8x + 5y = −9 and 5x + 8y = 9 →
  27. 27.3x + 4y = 23 and 3x − 3y = 9 →
  28. 28.2x + y = 12 and x + y = 8 →
  29. 29.2x − 2y = 4 and 2x − 4y = −2 →
  30. 30.5x − 5y = 10 and 4x + y = 38 →
  31. 31.x − 5y = −46 and x + 2y = 17 →
  32. 32.6x + 6y = 24 and 6x + 2y = 36 →
  33. 33.x − 6y = −23 and x + 3y = 22 →
  34. 34.4x + 2y = 18 and 4x − 5y = −3 →
  35. 35.6x + 9y = 69 and 9x + 6y = 36 →
  36. 36.5x + 2y = 14 and 3x + 2y = 10 →
  37. 37.3x + 5y = 27 and 5x + 3y = 29 →
  38. 38.2x + 3y = −16 and 3x + 2y = −4 →
  39. 39.5x + 3y = 37 and 5x − y = 41 →
  40. 40.3x + 2y = −20 and 4x + 2y = −28 →

Answer key

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

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