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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 768 · 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. 1.9x + 8y = 129 and 8x + 9y = 126 →
  2. 2.x + 4y = 11 and 6x − y = 41 →
  3. 3.9x + 6y = −30 and 6x + 9y = 0 →
  4. 4.4x − 2y = 18 and 3x + 6y = 21 →
  5. 5.5x + 6y = 62 and 2x − 3y = −13 →
  6. 6.x + 4y = 9 and 4x + y = −9 →
  7. 7.3x + 6y = −33 and 6x − 2y = −24 →
  8. 8.5x + 7y = 89 and 7x + 5y = 91 →
  9. 9.x + 2y = 17 and 3x + 3y = 24 →
  10. 10.9x + y = −43 and x + 9y = −67 →
  11. 11.x − 2y = −7 and x − 5y = −25 →
  12. 12.2x + y = −3 and 4x + 4y = −8 →
  13. 13.6x + y = −45 and 5x + 2y = −34 →
  14. 14.5x + 5y = 30 and 2x + y = 14 →
  15. 15.5x + 3y = 16 and 6x + 6y = 24 →
  16. 16.2x + 2y = 4 and 6x − 6y = 36 →
  17. 17.x + 5y = 26 and 5x + y = 34 →
  18. 18.3x + 5y = 11 and 3x + 6y = 12 →
  19. 19.3x + 7y = 47 and 7x + 3y = 43 →
  20. 20.3x + 3y = −12 and 2x + 6y = 12 →
  21. 21.2x + 3y = −10 and 5x + 3y = −34 →
  22. 22.3x + 2y = 10 and x + 5y = 12 →
  23. 23.4x + 5y = 31 and x + 4y = 5 →
  24. 24.4x + y = 10 and x + 3y = 19 →
  25. 25.x + 6y = 46 and 6x + y = −4 →
  26. 26.3x + 5y = −19 and 5x + 5y = −35 →
  27. 27.2x + 4y = 28 and 6x − 6y = −6 →
  28. 28.2x − y = 1 and 2x + y = 3 →
  29. 29.5x + 7y = 50 and 7x + 5y = 46 →
  30. 30.5x + 3y = −30 and 5x − 5y = −70 →
  31. 31.2x + 5y = 43 and x − 5y = −16 →
  32. 32.9x + 2y = 62 and 2x + 9y = 48 →
  33. 33.7x + 3y = 11 and 3x + 7y = −41 →
  34. 34.2x − 3y = 4 and 6x − 4y = 22 →
  35. 35.5x + 6y = 9 and 6x + y = 48 →
  36. 36.7x + 6y = −20 and 6x + 7y = −6 →
  37. 37.6x + 2y = 42 and 2x − 2y = 30 →
  38. 38.2x + y = 1 and x + 2y = 11 →
  39. 39.2x − 5y = 26 and 6x + y = −18 →
  40. 40.x − 5y = 4 and 4x + 5y = −34 →

Answer key

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

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