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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 460 · 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 + 4y = 1 and 4x + y = −26 →
  2. 2.4x − 2y = 22 and 2x + y = 17 →
  3. 3.4x + 3y = 17 and 6x + 2y = 8 →
  4. 4.x − y = −1 and 2x + 6y = −18 →
  5. 5.2x + 5y = 18 and x + 6y = 23 →
  6. 6.2x + 3y = −5 and 3x + 2y = −5 →
  7. 7.5x + y = 10 and x + 5y = 26 →
  8. 8.5x − 3y = −9 and 2x + y = 14 →
  9. 9.5x + 5y = 75 and 6x + 3y = 63 →
  10. 10.x − 6y = 13 and 2x + y = 13 →
  11. 11.2x + 2y = −10 and 4x − 5y = −47 →
  12. 12.x + 4y = 45 and 3x + y = 36 →
  13. 13.4x + 7y = −75 and 7x + 4y = −57 →
  14. 14.9x + 3y = 21 and 3x + 9y = 15 →
  15. 15.2x − 6y = −54 and 4x + 3y = 12 →
  16. 16.8x + 3y = 51 and 3x + 8y = −29 →
  17. 17.4x + 3y = −13 and 4x − 6y = −22 →
  18. 18.6x + 4y = 60 and 4x + 4y = 48 →
  19. 19.6x + 3y = 54 and x + 2y = 18 →
  20. 20.6x + 5y = 17 and 2x − 6y = −48 →
  21. 21.5x − 6y = 69 and x + y = −6 →
  22. 22.x − y = −11 and 4x + 4y = −28 →
  23. 23.6x + 3y = −48 and 3x + 6y = −15 →
  24. 24.3x + y = −8 and x + 3y = 0 →
  25. 25.5x − 5y = −5 and x + y = 3 →
  26. 26.4x − 2y = 24 and 5x + 6y = 64 →
  27. 27.5x − y = −50 and 3x − 5y = −52 →
  28. 28.4x + y = 33 and x + 4y = 42 →
  29. 29.5x + 2y = 49 and 2x + 4y = 42 →
  30. 30.4x + 7y = 11 and 7x + 4y = 11 →
  31. 31.x + 8y = −17 and 8x + y = 53 →
  32. 32.6x + 4y = −56 and x + 6y = −20 →
  33. 33.6x + 9y = 75 and 9x + 6y = 75 →
  34. 34.3x + 4y = 13 and 4x + 3y = 15 →
  35. 35.3x + 2y = 37 and 2x + 3y = 38 →
  36. 36.6x + 3y = −48 and 3x + 6y = −15 →
  37. 37.x − 2y = 0 and 3x − 4y = 2 →
  38. 38.x + 3y = −36 and 3x + 2y = −45 →
  39. 39.6x + 3y = −12 and 2x + 2y = −12 →
  40. 40.2x + 6y = −24 and 6x + 2y = 8 →

Answer key

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

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