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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 240 · 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 + 3y = −1 and 3x + y = 21 →
  2. 2.2x + 3y = 15 and 4x − 3y = −33 →
  3. 3.3x + 2y = 20 and x + 3y = 9 →
  4. 4.5x − 2y = −15 and 6x + 4y = 14 →
  5. 5.8x + 2y = 40 and 2x + 8y = 40 →
  6. 6.9x + 8y = 94 and 8x + 9y = 93 →
  7. 7.4x + y = 2 and x + 4y = −7 →
  8. 8.6x + y = −5 and 4x + 3y = −1 →
  9. 9.8x + 9y = 69 and 9x + 8y = 67 →
  10. 10.4x − 3y = 1 and 5x − 4y = 0 →
  11. 11.x + 6y = 34 and 4x + y = 21 →
  12. 12.8x + 4y = 52 and 4x + 8y = 20 →
  13. 13.5x + 5y = 30 and 2x − 4y = −18 →
  14. 14.7x + 3y = 43 and 3x + 7y = 7 →
  15. 15.5x + 5y = 20 and 6x − 3y = 6 →
  16. 16.5x − y = 38 and 5x + 5y = 80 →
  17. 17.3x + y = −15 and x + 3y = 11 →
  18. 18.3x − 6y = 66 and 2x + 4y = −12 →
  19. 19.x + 2y = 9 and 5x + 5y = 25 →
  20. 20.5x + 8y = −74 and 8x + 5y = −56 →
  21. 21.5x + y = 47 and 4x + 4y = 60 →
  22. 22.8x + 9y = 30 and 9x + 8y = 38 →
  23. 23.3x + y = 31 and 2x + 4y = 34 →
  24. 24.x + 5y = 33 and 6x + 2y = 58 →
  25. 25.x + 4y = −24 and 5x − y = −15 →
  26. 26.6x − 3y = 57 and 5x + y = 16 →
  27. 27.3x + 5y = 7 and 6x + y = −4 →
  28. 28.8x + y = 30 and x + 8y = 51 →
  29. 29.6x + y = 56 and 4x + y = 38 →
  30. 30.2x − 3y = −25 and 2x − 2y = −16 →
  31. 31.4x − 2y = 2 and 6x + y = −33 →
  32. 32.2x + y = −8 and x + 2y = −13 →
  33. 33.x + 4y = −23 and x − 4y = 33 →
  34. 34.7x + y = 47 and x + 7y = 41 →
  35. 35.x + 5y = −18 and 3x + 3y = −6 →
  36. 36.5x + 2y = 48 and 2x + 5y = 57 →
  37. 37.x + 4y = −1 and 4x + y = −19 →
  38. 38.4x + 5y = −11 and 5x + 4y = −25 →
  39. 39.x + 6y = 17 and 6x − 5y = 20 →
  40. 40.3x − 5y = −32 and 6x − 2y = −8 →

Answer key

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

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