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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 492 · 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 + 6y = 22 and 6x + 4y = 18 →
  2. 2.4x + 5y = 41 and 3x − 4y = −39 →
  3. 3.2x + 8y = 28 and 8x + 2y = 52 →
  4. 4.4x + y = −5 and 3x + 2y = 0 →
  5. 5.2x + 9y = −56 and 9x + 2y = −21 →
  6. 6.6x − y = 26 and 3x − 5y = −5 →
  7. 7.6x + 5y = 57 and x + 6y = 25 →
  8. 8.6x + y = 46 and x − 3y = 33 →
  9. 9.5x + y = 14 and 2x + 6y = 0 →
  10. 10.2x + 3y = 32 and x − 5y = −36 →
  11. 11.6x + 2y = 32 and 2x + 6y = 16 →
  12. 12.4x − 5y = 31 and 5x − 3y = 42 →
  13. 13.2x + y = 13 and x + 2y = 5 →
  14. 14.4x + 5y = 14 and 6x + 6y = 24 →
  15. 15.3x − 2y = 5 and 3x + 6y = −3 →
  16. 16.4x − 6y = −34 and 4x + 2y = 6 →
  17. 17.7x + 2y = 51 and 2x + 7y = −24 →
  18. 18.3x + 4y = 24 and 4x + 3y = 25 →
  19. 19.x + 6y = 23 and 6x + y = −37 →
  20. 20.2x − y = −16 and 6x + 4y = −6 →
  21. 21.4x + 3y = −6 and 3x + 4y = 6 →
  22. 22.2x − y = 19 and x − y = 13 →
  23. 23.x − y = −11 and 2x − 5y = −37 →
  24. 24.4x + 3y = −2 and 3x − 5y = 13 →
  25. 25.x + 6y = −33 and 5x − 3y = 0 →
  26. 26.x + 6y = 9 and x + y = 4 →
  27. 27.4x − 3y = −17 and 6x + 2y = −6 →
  28. 28.7x + 2y = 16 and 2x + 7y = 11 →
  29. 29.3x − 2y = −11 and 5x − 6y = −21 →
  30. 30.3x + y = 6 and 2x + 3y = −10 →
  31. 31.2x + 6y = 2 and 6x − 2y = −14 →
  32. 32.x + 9y = 60 and 9x + y = 60 →
  33. 33.x + y = −5 and 4x + 3y = −22 →
  34. 34.6x − 4y = −74 and 4x − 6y = −66 →
  35. 35.6x + 3y = 51 and 2x − y = 19 →
  36. 36.8x + 9y = 76 and 9x + 8y = 77 →
  37. 37.3x − 3y = 51 and 2x + 2y = 2 →
  38. 38.6x + 2y = 22 and 3x − y = 7 →
  39. 39.9x + 3y = 60 and 3x + 9y = 36 →
  40. 40.5x − 3y = 9 and 5x − y = 23 →

Answer key

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

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