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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 638 · 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. 1.6x − 5y = −42 and 6x + 6y = 24 →
  2. 2.4x − 3y = −10 and x − 6y = −34 →
  3. 3.3x + y = 7 and x + 3y = 13 →
  4. 4.7x + 9y = 114 and 9x + 7y = 110 →
  5. 5.2x + y = 16 and 6x + 6y = 72 →
  6. 6.x + 4y = 23 and 4x + 5y = 37 →
  7. 7.2x + 2y = 22 and 6x + 5y = 61 →
  8. 8.7x + y = 23 and x + 7y = 17 →
  9. 9.2x + 6y = 50 and 2x + y = 15 →
  10. 10.5x + 3y = −28 and 6x + 6y = −36 →
  11. 11.x + y = 7 and x + 6y = 27 →
  12. 12.6x + 4y = 44 and x − 3y = −11 →
  13. 13.8x + 9y = −64 and 9x + 8y = −55 →
  14. 14.6x − 6y = −72 and 2x − 3y = −29 →
  15. 15.6x + 2y = −18 and x + 3y = 13 →
  16. 16.x + 4y = −29 and 2x + 3y = −13 →
  17. 17.3x + y = 7 and 5x + 6y = 3 →
  18. 18.4x + 6y = −26 and 6x + 4y = −44 →
  19. 19.3x + 4y = 46 and 4x + 3y = 45 →
  20. 20.2x − 5y = −23 and 6x − 6y = −24 →
  21. 21.2x + 2y = 14 and 3x + y = 19 →
  22. 22.2x + 3y = 4 and 5x − 2y = −47 →
  23. 23.2x + 6y = 10 and x + 5y = 9 →
  24. 24.4x + y = 18 and x − 3y = 24 →
  25. 25.2x + 2y = 2 and 6x − 4y = 46 →
  26. 26.6x − 5y = 3 and 2x + 4y = 18 →
  27. 27.4x + 3y = 49 and 3x + 4y = 49 →
  28. 28.5x − 2y = −1 and 3x + 6y = 57 →
  29. 29.4x − 2y = −32 and x − 5y = −17 →
  30. 30.8x + 3y = −55 and 3x + 8y = 0 →
  31. 31.5x + y = −37 and x + 5y = 31 →
  32. 32.4x + y = −22 and 2x + y = −10 →
  33. 33.x + 6y = 41 and 2x − 3y = −38 →
  34. 34.6x − 5y = −28 and 2x − 3y = −20 →
  35. 35.5x − 4y = −6 and x + 2y = −4 →
  36. 36.4x + 2y = 6 and 4x − 2y = 2 →
  37. 37.3x + 9y = 0 and 9x + 3y = −48 →
  38. 38.9x + 4y = −82 and 4x + 9y = −87 →
  39. 39.x + 2y = −3 and 6x − y = −57 →
  40. 40.4x + 5y = 31 and 5x + 4y = 32 →

Answer key

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

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