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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 298 · 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. 1.5x + y = −11 and 2x + 5y = 14 →
  2. 2.x − 2y = −2 and x + 2y = 10 →
  3. 3.2x + 6y = 4 and 6x + 2y = −20 →
  4. 4.6x + y = 15 and 4x − y = 25 →
  5. 5.2x + 5y = −26 and x + y = −10 →
  6. 6.x + 4y = 11 and 2x − 2y = 2 →
  7. 7.4x + 6y = −42 and 2x + y = −3 →
  8. 8.x + 2y = 8 and 4x + 2y = 2 →
  9. 9.5x + y = 19 and 4x − 5y = −8 →
  10. 10.5x − y = 33 and 4x + 5y = 9 →
  11. 11.8x + 7y = 18 and 7x + 8y = 27 →
  12. 12.4x − 2y = −42 and 3x − 6y = −45 →
  13. 13.5x + 9y = 42 and 9x + 5y = 42 →
  14. 14.x + 2y = −13 and 2x + y = −5 →
  15. 15.5x − y = −14 and 2x + 3y = 8 →
  16. 16.5x + 6y = 19 and 3x + 3y = 9 →
  17. 17.6x + 3y = −3 and 3x + 4y = 11 →
  18. 18.2x + 4y = 22 and 4x + y = 23 →
  19. 19.x + 4y = 40 and 6x + 2y = 64 →
  20. 20.3x + 3y = 3 and 5x + 3y = −3 →
  21. 21.9x + 7y = 70 and 7x + 9y = 58 →
  22. 22.2x + 6y = 48 and 6x + 2y = 64 →
  23. 23.x + 9y = 18 and 9x + y = 82 →
  24. 24.2x + 9y = −6 and 9x + 2y = 50 →
  25. 25.9x + 2y = 9 and 2x + 9y = 79 →
  26. 26.8x + 5y = −55 and 5x + 8y = −49 →
  27. 27.4x + 5y = 72 and x + y = 16 →
  28. 28.2x + 8y = 14 and 8x + 2y = 26 →
  29. 29.3x + 5y = 58 and 3x − 5y = −22 →
  30. 30.6x + 4y = −18 and 2x + 5y = −28 →
  31. 31.2x − 6y = 2 and 2x + 4y = 22 →
  32. 32.5x − 3y = −8 and 3x + 3y = 24 →
  33. 33.4x − 3y = −7 and 2x + 5y = 29 →
  34. 34.2x + 7y = −6 and 7x + 2y = 24 →
  35. 35.4x + 7y = 71 and 7x + 4y = 50 →
  36. 36.4x + 3y = −21 and 6x − 4y = −40 →
  37. 37.3x + 2y = 29 and 5x + y = 39 →
  38. 38.5x + y = 31 and x + 4y = 29 →
  39. 39.7x + 2y = −24 and 2x + 7y = 6 →
  40. 40.3x + 6y = −57 and 4x + y = −27 →

Answer key

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

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