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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 54 · 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 + 6y = 5 and 6x + 6y = 0 →
  2. 2.2x − 5y = 27 and 2x + 2y = −36 →
  3. 3.3x + 5y = 24 and 5x + 3y = 24 →
  4. 4.5x − 5y = 15 and x + 4y = −7 →
  5. 5.9x + 4y = 99 and 4x + 9y = 109 →
  6. 6.6x + 2y = 40 and x − 5y = −20 →
  7. 7.x + 9y = 26 and 9x + y = −6 →
  8. 8.4x + 2y = 30 and x + y = 11 →
  9. 9.4x + y = −10 and x − y = −5 →
  10. 10.5x + 9y = 65 and 9x + 5y = 61 →
  11. 11.3x + 8y = −33 and 8x + 3y = −33 →
  12. 12.4x + y = 14 and 6x + y = 22 →
  13. 13.x + y = −5 and 6x + 2y = −14 →
  14. 14.5x − 4y = 37 and 2x + 3y = 24 →
  15. 15.x + 2y = −7 and 2x + 2y = 0 →
  16. 16.x + 4y = 21 and x − 5y = −42 →
  17. 17.6x + y = 41 and 3x + 3y = 18 →
  18. 18.2x + 6y = 18 and 3x − 3y = 3 →
  19. 19.5x + 6y = −94 and 6x + 5y = −93 →
  20. 20.6x + 3y = −39 and 3x + 6y = −15 →
  21. 21.3x + 5y = −22 and 5x + 3y = 6 →
  22. 22.3x + 8y = −19 and 8x + 3y = −69 →
  23. 23.5x + 3y = 62 and x − y = −2 →
  24. 24.2x + y = 17 and 2x + 2y = 18 →
  25. 25.6x − y = 32 and 3x − y = 17 →
  26. 26.6x + 4y = 22 and 6x + y = 10 →
  27. 27.6x + 3y = 0 and 3x + 6y = 27 →
  28. 28.8x + 9y = 76 and 9x + 8y = 77 →
  29. 29.3x + 6y = −30 and 5x + 5y = −5 →
  30. 30.5x + 3y = 18 and 3x + 5y = 14 →
  31. 31.x + y = −3 and 5x + y = 17 →
  32. 32.5x + 5y = 40 and 4x + 2y = 20 →
  33. 33.4x + 2y = 34 and 6x + 6y = 78 →
  34. 34.6x + 4y = −8 and 4x + 2y = −10 →
  35. 35.2x + 6y = 38 and 6x + 2y = 18 →
  36. 36.3x + 2y = 19 and 2x + 3y = 16 →
  37. 37.3x − 3y = 15 and 2x + 2y = 6 →
  38. 38.3x + 2y = 7 and 6x + 2y = 10 →
  39. 39.3x + 2y = 26 and x + 5y = 13 →
  40. 40.6x + y = 13 and x + y = 8 →

Answer key

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

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