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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 826 · 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 = −25 and 5x + 2y = −5 →
  2. 2.6x + 3y = 48 and x − 2y = 13 →
  3. 3.5x + 4y = 7 and 4x + y = 21 →
  4. 4.8x + 4y = −24 and 4x + 8y = 24 →
  5. 5.3x + 5y = −13 and 3x + 3y = −9 →
  6. 6.2x + 5y = 33 and 3x − 6y = −72 →
  7. 7.x + 8y = 31 and 8x + y = 59 →
  8. 8.3x + 3y = −3 and 6x − y = 29 →
  9. 9.3x + 2y = −19 and 2x + 3y = −16 →
  10. 10.2x − 4y = 0 and 2x + 4y = 8 →
  11. 11.5x + 8y = −1 and 8x + 5y = 14 →
  12. 12.2x + y = 19 and 6x + 4y = 62 →
  13. 13.6x − 4y = 2 and 5x − 3y = 0 →
  14. 14.5x + 3y = 29 and 3x + 5y = 27 →
  15. 15.6x + 5y = 4 and 5x + 6y = 18 →
  16. 16.5x + y = 39 and 4x − 6y = 72 →
  17. 17.4x + 6y = 54 and 6x − y = 11 →
  18. 18.9x + y = 65 and x + 9y = 25 →
  19. 19.4x + 6y = −14 and 3x − 4y = −36 →
  20. 20.9x + 8y = −74 and 8x + 9y = −79 →
  21. 21.x + 3y = −3 and x + y = 3 →
  22. 22.3x + 3y = 36 and 4x − 6y = −12 →
  23. 23.x + 5y = 12 and 6x + y = −15 →
  24. 24.5x + y = 32 and 2x + 2y = 8 →
  25. 25.2x + 2y = 6 and 2x + y = 5 →
  26. 26.4x + y = −4 and x + 5y = 18 →
  27. 27.6x + 7y = 47 and 7x + 6y = 44 →
  28. 28.x + 5y = 1 and 5x − 2y = −22 →
  29. 29.4x + 3y = 21 and 2x − 3y = −3 →
  30. 30.2x + 9y = 42 and 9x + 2y = 35 →
  31. 31.3x + 6y = 18 and 6x − 5y = 19 →
  32. 32.3x + 2y = −7 and 2x + 3y = 7 →
  33. 33.x − y = 2 and 3x + y = 18 →
  34. 34.x − 3y = 19 and 6x + 5y = −24 →
  35. 35.7x + 6y = 7 and 6x + 7y = −7 →
  36. 36.x + 3y = −18 and x − 5y = 38 →
  37. 37.4x − 4y = 20 and x + 3y = 9 →
  38. 38.x + 2y = −9 and 2x + y = 3 →
  39. 39.6x + y = 49 and 4x + 2y = 26 →
  40. 40.4x + 4y = −44 and 5x + 6y = −64 →

Answer key

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

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