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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 75 · 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.x + 2y = 8 and x − y = 5 →
  2. 2.x + 6y = 39 and 6x + y = 24 →
  3. 3.5x − 2y = 33 and 4x + 4y = 32 →
  4. 4.5x + 9y = −26 and 9x + 5y = −58 →
  5. 5.6x − 4y = 18 and 3x + 5y = −12 →
  6. 6.4x + 3y = −7 and x − 2y = 12 →
  7. 7.x + 4y = 1 and 4x + y = −11 →
  8. 8.5x + 6y = 17 and x − 2y = 13 →
  9. 9.5x − 5y = 80 and 3x − y = 34 →
  10. 10.2x − y = 5 and 5x + 4y = 6 →
  11. 11.4x + 6y = 24 and 4x − 6y = −72 →
  12. 12.x + 6y = 26 and 6x + y = 16 →
  13. 13.4x + 3y = 6 and x + 6y = 33 →
  14. 14.5x + 4y = 1 and 4x + 5y = 17 →
  15. 15.x + 5y = 32 and 5x + 2y = 22 →
  16. 16.6x + 7y = 68 and 7x + 6y = 75 →
  17. 17.3x + 4y = −17 and x + y = −6 →
  18. 18.4x + 6y = 14 and 6x + 4y = 36 →
  19. 19.5x + 3y = 4 and 4x + 4y = 0 →
  20. 20.2x + 3y = 9 and 6x − 3y = −81 →
  21. 21.2x + 5y = 1 and 3x + 6y = 6 →
  22. 22.4x + 8y = 48 and 8x + 4y = 48 →
  23. 23.5x + y = 4 and 3x + 4y = 33 →
  24. 24.7x + 6y = 26 and 6x + 7y = 13 →
  25. 25.7x + 8y = 82 and 8x + 7y = 83 →
  26. 26.9x + 7y = 99 and 7x + 9y = 109 →
  27. 27.3x + 5y = 27 and 6x + y = −27 →
  28. 28.4x + 3y = 11 and 2x + y = 5 →
  29. 29.6x − 6y = −36 and 2x + 4y = 42 →
  30. 30.4x − 6y = −44 and 2x − 2y = −16 →
  31. 31.3x − 3y = −15 and 4x + 4y = 36 →
  32. 32.6x − 3y = −30 and 2x + 2y = −16 →
  33. 33.6x + 9y = 96 and 9x + 6y = 99 →
  34. 34.6x − 5y = −76 and 5x + 2y = −14 →
  35. 35.4x + 4y = −24 and 4x + y = −30 →
  36. 36.7x + y = −6 and x + 7y = 54 →
  37. 37.2x − y = 15 and 4x + 3y = 45 →
  38. 38.6x + 6y = −48 and 2x + y = −15 →
  39. 39.6x + 4y = 24 and 4x + 5y = 2 →
  40. 40.x + 4y = 16 and 6x − 6y = 6 →

Answer key

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

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