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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 719 · 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. 1.4x + 5y = 5 and 5x + 4y = −5 →
  2. 2.7x + 6y = 12 and 6x + 7y = 27 →
  3. 3.5x + 2y = 19 and 2x + 5y = −5 →
  4. 4.3x − 2y = −28 and 2x + 4y = −8 →
  5. 5.8x + 5y = 7 and 5x + 8y = −20 →
  6. 6.x + 9y = 71 and 9x + y = 79 →
  7. 7.6x + 2y = −32 and 4x + 5y = −36 →
  8. 8.x − 2y = −9 and 5x + 5y = −30 →
  9. 9.8x + 7y = −3 and 7x + 8y = −12 →
  10. 10.3x − 4y = 13 and 2x + 3y = 3 →
  11. 11.2x − 3y = −8 and 4x − y = −26 →
  12. 12.4x + 7y = −1 and 7x + 4y = 23 →
  13. 13.4x − y = 22 and 3x − y = 16 →
  14. 14.5x + y = 10 and x + 5y = 26 →
  15. 15.6x + 2y = 22 and 5x + 2y = 21 →
  16. 16.4x + 9y = 63 and 9x + 4y = 93 →
  17. 17.x + 3y = −18 and 5x − 6y = 57 →
  18. 18.8x + y = 36 and x + 8y = 36 →
  19. 19.x + 4y = 41 and 6x + 3y = 78 →
  20. 20.5x − 6y = 24 and 4x + 4y = 28 →
  21. 21.2x + 2y = −8 and x − 2y = −16 →
  22. 22.6x + 5y = 27 and 6x − 4y = 0 →
  23. 23.4x − 3y = −44 and 2x + 2y = 6 →
  24. 24.4x − 5y = 32 and 2x + y = −12 →
  25. 25.6x + 5y = 49 and 3x + 2y = 22 →
  26. 26.3x + y = 8 and 5x + y = 10 →
  27. 27.5x − 4y = −19 and x + 6y = −31 →
  28. 28.4x + 4y = −32 and 6x + 4y = −50 →
  29. 29.5x + y = 37 and 3x + 3y = 39 →
  30. 30.6x + 2y = −34 and x − 5y = 21 →
  31. 31.3x + 4y = 13 and 2x − 4y = 2 →
  32. 32.5x + 2y = 29 and 4x − y = 5 →
  33. 33.3x + y = 32 and 5x − y = 40 →
  34. 34.3x − 2y = 27 and 4x + 5y = −33 →
  35. 35.2x + 5y = 51 and 5x + 3y = 42 →
  36. 36.3x − y = 3 and 4x + 6y = 26 →
  37. 37.8x + y = 65 and x + 8y = 16 →
  38. 38.6x + 9y = 66 and 9x + 6y = 54 →
  39. 39.6x + 5y = −27 and 2x − 5y = 51 →
  40. 40.x + 5y = 34 and 5x + 6y = 56 →

Answer key

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

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