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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 505 · 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. 1.8x + 9y = 47 and 9x + 8y = 38 →
  2. 2.9x + 5y = 73 and 5x + 9y = 53 →
  3. 3.3x + y = 33 and 5x − y = 39 →
  4. 4.5x + 8y = 104 and 8x + 5y = 104 →
  5. 5.9x + 3y = 33 and 3x + 9y = 51 →
  6. 6.5x + 9y = 86 and 9x + 5y = 54 →
  7. 7.5x + y = 13 and 3x − 6y = −45 →
  8. 8.3x + y = −7 and 6x − 6y = −6 →
  9. 9.2x + 2y = 12 and 3x − y = 2 →
  10. 10.3x − 3y = 6 and x + 2y = 8 →
  11. 11.4x − 5y = 21 and 4x + 2y = 14 →
  12. 12.7x + 3y = −3 and 3x + 7y = 33 →
  13. 13.x + 7y = −37 and 7x + y = 29 →
  14. 14.x + 3y = 17 and 5x − 5y = −15 →
  15. 15.3x + y = 32 and 2x − 3y = 3 →
  16. 16.2x − 5y = −33 and x + 6y = 43 →
  17. 17.x − 2y = 2 and 3x + 2y = −26 →
  18. 18.2x − y = −1 and 3x + y = −4 →
  19. 19.5x + y = 32 and 6x + 3y = 51 →
  20. 20.4x + 9y = −1 and 9x + 4y = −51 →
  21. 21.6x + 8y = 24 and 8x + 6y = 4 →
  22. 22.2x + y = 22 and 6x + y = 54 →
  23. 23.x + 2y = 13 and 6x − 5y = 10 →
  24. 24.6x + 9y = −36 and 9x + 6y = −69 →
  25. 25.9x + 4y = 35 and 4x + 9y = 30 →
  26. 26.8x + 6y = 50 and 6x + 8y = 62 →
  27. 27.5x + 7y = 87 and 7x + 5y = 93 →
  28. 28.3x − 3y = 27 and 5x + 6y = 12 →
  29. 29.5x − y = 12 and 2x − y = 9 →
  30. 30.6x − 5y = 31 and 4x − 6y = 18 →
  31. 31.3x + 7y = 36 and 7x + 3y = 4 →
  32. 32.6x − 3y = 45 and 2x + 2y = 24 →
  33. 33.4x + 4y = −8 and 3x − 3y = 24 →
  34. 34.9x + 2y = 99 and 2x + 9y = 99 →
  35. 35.7x + 3y = −15 and 3x + 7y = 5 →
  36. 36.4x + 2y = 12 and 3x − 4y = −13 →
  37. 37.6x − 2y = −36 and 5x − 4y = −9 →
  38. 38.6x + 4y = 34 and 4x + 6y = 26 →
  39. 39.x + 9y = 49 and 9x + y = −39 →
  40. 40.6x + y = 41 and 4x + 2y = 26 →

Answer key

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

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