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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 820 · 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 = −9 and 4x + 2y = 4 →
  2. 2.3x + 8y = −49 and 8x + 3y = 16 →
  3. 3.x + 6y = 40 and x − 3y = −14 →
  4. 4.x + y = 9 and x + 5y = 41 →
  5. 5.5x + 4y = 3 and 2x + 3y = 4 →
  6. 6.6x + y = 43 and 2x − 5y = 9 →
  7. 7.4x + y = −25 and 3x − 4y = 5 →
  8. 8.7x + 8y = 70 and 8x + 7y = 65 →
  9. 9.4x + 7y = 18 and 7x + 4y = 15 →
  10. 10.8x + 2y = −40 and 2x + 8y = 50 →
  11. 11.5x + 4y = −46 and 4x + y = −28 →
  12. 12.x + 5y = 24 and 5x + 5y = 40 →
  13. 13.2x + 3y = 9 and 2x − 3y = 3 →
  14. 14.2x − 3y = −33 and 2x + 5y = 39 →
  15. 15.x + 5y = 48 and 3x − 5y = −36 →
  16. 16.2x + 4y = 28 and 2x + 3y = 24 →
  17. 17.x + y = −4 and 4x − 6y = 44 →
  18. 18.3x − 2y = 16 and x + 5y = −6 →
  19. 19.3x + 2y = 29 and 2x + 3y = 26 →
  20. 20.3x − 6y = −15 and 4x + y = −2 →
  21. 21.4x − 2y = 18 and 4x + 4y = 60 →
  22. 22.6x − y = 47 and 5x − 4y = 36 →
  23. 23.2x + 9y = 45 and 9x + 2y = 87 →
  24. 24.6x − 4y = −36 and 5x − 2y = −22 →
  25. 25.4x + 2y = 12 and x − 6y = −23 →
  26. 26.4x + 5y = 46 and 6x − 5y = 44 →
  27. 27.9x + 2y = 31 and 2x + 9y = −53 →
  28. 28.x − 5y = −18 and 5x + 4y = −3 →
  29. 29.6x + 6y = 48 and 3x + 2y = 23 →
  30. 30.2x + 2y = −14 and 5x + y = −27 →
  31. 31.x + 6y = 17 and 3x − 3y = −33 →
  32. 32.2x + 2y = 28 and 4x + y = 32 →
  33. 33.2x − 5y = 12 and 4x + 5y = −36 →
  34. 34.x − y = −5 and 5x − 6y = −34 →
  35. 35.5x + 3y = 10 and 5x − 4y = −25 →
  36. 36.8x + 5y = 53 and 5x + 8y = 38 →
  37. 37.3x + 2y = −3 and 2x + 3y = 13 →
  38. 38.4x + 4y = 8 and 2x − 4y = −26 →
  39. 39.5x + y = 28 and x + 5y = −4 →
  40. 40.2x + 3y = 33 and 6x + y = 27 →

Answer key

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

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