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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 94 · 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. 1.2x − 4y = −28 and 6x + 3y = −9 →
  2. 2.3x + 4y = 6 and 4x + 3y = 1 →
  3. 3.x + 7y = 68 and 7x + y = 44 →
  4. 4.x − 4y = −7 and x + y = 3 →
  5. 5.4x + 3y = 15 and 2x − 5y = 27 →
  6. 6.x + 3y = −6 and 2x + 5y = −9 →
  7. 7.5x + 6y = 82 and 6x + 3y = 69 →
  8. 8.6x + 7y = 40 and 7x + 6y = 38 →
  9. 9.6x + y = 56 and x + 6y = 21 →
  10. 10.5x + 3y = 57 and 2x + 4y = 48 →
  11. 11.x + 5y = 32 and 2x + 5y = 24 →
  12. 12.5x + 7y = −98 and 7x + 5y = −94 →
  13. 13.x − 2y = 15 and 5x − 2y = 27 →
  14. 14.8x + 4y = 68 and 4x + 8y = 76 →
  15. 15.4x + 5y = 38 and 2x + 5y = 34 →
  16. 16.3x − 3y = −15 and x + 4y = 5 →
  17. 17.6x + 2y = 28 and 2x + 6y = 20 →
  18. 18.3x + y = 19 and 4x − 4y = 20 →
  19. 19.8x + 9y = 14 and 9x + 8y = 20 →
  20. 20.5x + 2y = −28 and x − 2y = −8 →
  21. 21.2x + 3y = 14 and 5x + 5y = 20 →
  22. 22.5x + 4y = 26 and 6x + 6y = 30 →
  23. 23.3x + 9y = 45 and 9x + 3y = −9 →
  24. 24.3x + y = 8 and x + 3y = 16 →
  25. 25.6x + 3y = 72 and x + 3y = 27 →
  26. 26.5x + 3y = 25 and 2x + 2y = 14 →
  27. 27.2x + 5y = 26 and 6x − 3y = −66 →
  28. 28.5x + 3y = −1 and 3x − 4y = 11 →
  29. 29.4x + y = 2 and x + 4y = 23 →
  30. 30.3x + 6y = 33 and 4x + 2y = −10 →
  31. 31.7x + 6y = −41 and 6x + 7y = −50 →
  32. 32.2x + 3y = 3 and 4x + y = 31 →
  33. 33.2x + 8y = 26 and 8x + 2y = 74 →
  34. 34.4x − 6y = 18 and 4x − 5y = 19 →
  35. 35.2x − 5y = 1 and 6x + 5y = 63 →
  36. 36.5x + 3y = 63 and x + y = 15 →
  37. 37.3x + 3y = 15 and 5x − 5y = −5 →
  38. 38.7x + 6y = −11 and 6x + 7y = −15 →
  39. 39.5x + 6y = 75 and 6x + 5y = 79 →
  40. 40.4x + 2y = 6 and x + y = 1 →

Answer key

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

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