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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 613 · 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. 1.3x + 5y = 12 and 4x + 5y = 11 →
  2. 2.4x + 8y = −64 and 8x + 4y = −80 →
  3. 3.6x + 5y = −27 and 5x + 6y = −17 →
  4. 4.4x + 6y = −34 and 5x + 5y = −40 →
  5. 5.2x − 4y = −10 and 6x + 3y = 45 →
  6. 6.6x − y = 31 and x + 4y = −24 →
  7. 7.x + 3y = 20 and x + 5y = 32 →
  8. 8.8x + 5y = −44 and 5x + 8y = −8 →
  9. 9.2x + 7y = 37 and 7x + 2y = 62 →
  10. 10.4x + 7y = −6 and 7x + 4y = −27 →
  11. 11.x + 6y = −14 and 6x + y = −49 →
  12. 12.x + 7y = 46 and 7x + y = 34 →
  13. 13.5x + 5y = 20 and 6x + 2y = 16 →
  14. 14.6x + y = −29 and 5x − 3y = −28 →
  15. 15.x + 4y = 15 and 4x + 5y = 27 →
  16. 16.6x + 3y = 45 and x + 5y = 21 →
  17. 17.2x + 6y = 72 and 6x − 3y = 27 →
  18. 18.3x + 6y = 36 and 6x + 3y = 45 →
  19. 19.2x + 2y = −24 and 5x + 6y = −63 →
  20. 20.3x − 5y = −34 and 2x + 3y = 28 →
  21. 21.7x + 9y = 42 and 9x + 7y = 22 →
  22. 22.x + 4y = 24 and 3x − 2y = 16 →
  23. 23.8x + 3y = 11 and 3x + 8y = −44 →
  24. 24.2x + 3y = −30 and 5x + 6y = −66 →
  25. 25.4x − 3y = 13 and 2x − 5y = 31 →
  26. 26.3x + 6y = −63 and 5x − 4y = 7 →
  27. 27.7x + 6y = −37 and 6x + 7y = −41 →
  28. 28.x + 2y = 12 and 2x + 6y = 42 →
  29. 29.x − 4y = −18 and 2x + 5y = 3 →
  30. 30.5x + 6y = 69 and 2x + 2y = 26 →
  31. 31.9x + 4y = 43 and 4x + 9y = 48 →
  32. 32.2x − 4y = −6 and 5x + y = 51 →
  33. 33.5x + 9y = 36 and 9x + 5y = 76 →
  34. 34.6x − 5y = 25 and 5x + 6y = 31 →
  35. 35.x + 4y = 30 and 3x + 2y = 20 →
  36. 36.2x + 3y = 1 and 3x + 2y = 14 →
  37. 37.2x + 3y = −5 and 3x − y = 9 →
  38. 38.x + 2y = 19 and 4x − 5y = −41 →
  39. 39.5x + y = 9 and 6x + y = 12 →
  40. 40.x + 2y = 7 and 2x + y = −1 →

Answer key

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

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