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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 470 · 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 + 2y = 48 and 2x + 4y = 48 →
  2. 2.6x − 5y = −23 and 6x + 6y = −12 →
  3. 3.4x + 6y = 66 and 5x + 3y = 51 →
  4. 4.3x + 2y = −22 and 3x − 2y = 10 →
  5. 5.5x + y = 48 and x + y = 12 →
  6. 6.x − 5y = 41 and 3x + 6y = −45 →
  7. 7.6x + 9y = −45 and 9x + 6y = 0 →
  8. 8.x + 3y = −8 and 2x + 2y = −4 →
  9. 9.x + 5y = 11 and 4x + 3y = 27 →
  10. 10.2x + y = −1 and 4x − 3y = −37 →
  11. 11.3x − y = 2 and 5x + 4y = 9 →
  12. 12.3x + y = −2 and x + 3y = 18 →
  13. 13.2x + 6y = 50 and 6x + 2y = 22 →
  14. 14.x + 4y = 13 and x − 3y = −1 →
  15. 15.x − 6y = 38 and 2x − 6y = 46 →
  16. 16.3x + 2y = 9 and 4x + 3y = 11 →
  17. 17.6x + 7y = 41 and 7x + 6y = 37 →
  18. 18.3x − 5y = 33 and x + y = −5 →
  19. 19.6x + 3y = 15 and 6x + 6y = 12 →
  20. 20.3x + 9y = 99 and 9x + 3y = 105 →
  21. 21.9x + 6y = −21 and 6x + 9y = −24 →
  22. 22.6x + 2y = −48 and x − 5y = −24 →
  23. 23.2x + 3y = 7 and 3x + 2y = −7 →
  24. 24.x + 6y = 24 and 5x + 2y = 36 →
  25. 25.9x + 7y = −96 and 7x + 9y = −96 →
  26. 26.2x + 4y = 22 and 6x + 3y = 30 →
  27. 27.8x + 4y = 48 and 4x + 8y = 0 →
  28. 28.4x + 7y = 99 and 7x + 4y = 99 →
  29. 29.5x − 4y = −10 and 5x + 3y = 25 →
  30. 30.5x + 3y = −34 and 3x + 5y = −14 →
  31. 31.x − 6y = −33 and 6x + 5y = 48 →
  32. 32.3x + 6y = −18 and 6x + 3y = 27 →
  33. 33.6x + 2y = 14 and 5x − 6y = −19 →
  34. 34.9x + 7y = 91 and 7x + 9y = 85 →
  35. 35.x − 4y = 38 and 2x + 3y = −12 →
  36. 36.4x + 7y = 39 and 7x + 4y = 60 →
  37. 37.3x + 9y = 69 and 9x + 3y = 87 →
  38. 38.5x − 2y = 11 and 6x − 4y = 2 →
  39. 39.3x + 7y = −17 and 7x + 3y = −53 →
  40. 40.x + 6y = 22 and 6x + y = −8 →

Answer key

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

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