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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 4 · 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. 1.9x + 6y = 18 and 6x + 9y = −18 →
  2. 2.3x − 4y = −12 and 4x + 6y = 52 →
  3. 3.x + 3y = 18 and x − 2y = −2 →
  4. 4.x + 2y = −1 and 2x + y = 13 →
  5. 5.x + 3y = 31 and 2x + 2y = 26 →
  6. 6.3x + 5y = −43 and 5x + 3y = −29 →
  7. 7.6x + 3y = −33 and 3x + 6y = −21 →
  8. 8.x + 3y = 35 and 4x + 3y = 59 →
  9. 9.9x + 7y = −4 and 7x + 9y = −28 →
  10. 10.7x + 5y = −52 and 5x + 7y = −44 →
  11. 11.5x + 6y = 13 and 6x + 6y = 12 →
  12. 12.x − 6y = 53 and 6x + 2y = −24 →
  13. 13.6x + 5y = −57 and 3x + y = −15 →
  14. 14.8x + 2y = −36 and 2x + 8y = 6 →
  15. 15.6x + 2y = 30 and 2x + 6y = 42 →
  16. 16.x + 2y = −5 and 6x + 6y = 6 →
  17. 17.6x + 2y = 12 and 3x − 6y = −15 →
  18. 18.x − 4y = −34 and 2x − y = −5 →
  19. 19.4x + 6y = 60 and 6x + 6y = 72 →
  20. 20.2x − y = 3 and 6x + y = 5 →
  21. 21.3x + y = −1 and x + 3y = 5 →
  22. 22.2x + 8y = 82 and 8x + 2y = 58 →
  23. 23.2x + y = −1 and 5x + 4y = 5 →
  24. 24.3x + 4y = −16 and 2x + 5y = −27 →
  25. 25.7x + 5y = 52 and 5x + 7y = 44 →
  26. 26.6x + 5y = 62 and 5x + 6y = 59 →
  27. 27.2x + 9y = 41 and 9x + 2y = 69 →
  28. 28.x + y = −4 and x − 5y = 50 →
  29. 29.5x + 4y = −8 and 4x + 5y = 8 →
  30. 30.9x + 7y = 135 and 7x + 9y = 137 →
  31. 31.6x + 5y = 4 and 5x + 6y = 7 →
  32. 32.6x − y = 45 and x + 5y = 54 →
  33. 33.3x − y = −3 and 6x − 5y = −33 →
  34. 34.2x − 3y = 32 and 2x + 2y = −8 →
  35. 35.5x − y = 39 and 4x + y = 33 →
  36. 36.5x − 6y = 84 and 4x − 5y = 69 →
  37. 37.6x + 5y = 56 and 4x − 2y = 16 →
  38. 38.2x − 4y = −8 and 4x + 2y = 34 →
  39. 39.5x + 3y = 17 and 3x + 5y = 23 →
  40. 40.8x + y = 28 and x + 8y = 35 →

Answer key

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

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