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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 282 · 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. 1.6x + 4y = −12 and 4x + 6y = 2 →
  2. 2.6x + 8y = 68 and 8x + 6y = 72 →
  3. 3.5x + 4y = 7 and 3x + 5y = −1 →
  4. 4.6x + 5y = 53 and 4x − 5y = 27 →
  5. 5.3x + 3y = 45 and 3x − 2y = 10 →
  6. 6.x − 2y = 12 and 4x + 6y = 20 →
  7. 7.6x + 7y = 50 and 7x + 6y = 41 →
  8. 8.3x + y = 11 and 2x + y = 8 →
  9. 9.x + y = 5 and 3x + 4y = 11 →
  10. 10.3x + 4y = 27 and 3x + 2y = 21 →
  11. 11.4x + 2y = 10 and 2x + 4y = 14 →
  12. 12.4x + 4y = 4 and 5x + y = −27 →
  13. 13.4x + 8y = 36 and 8x + 4y = 12 →
  14. 14.4x + 6y = −34 and 3x + 3y = −24 →
  15. 15.2x + y = 4 and x + 5y = −34 →
  16. 16.x + 2y = 11 and 3x + 2y = 29 →
  17. 17.2x − 3y = 6 and 3x + 2y = 35 →
  18. 18.4x + 3y = −10 and 3x + 4y = −18 →
  19. 19.8x + 3y = −29 and 3x + 8y = 51 →
  20. 20.2x + 7y = 18 and 7x + 2y = 18 →
  21. 21.2x + 6y = 38 and 4x + y = 32 →
  22. 22.2x − 2y = −4 and 2x + 3y = 16 →
  23. 23.x + 6y = 15 and 3x − 2y = 5 →
  24. 24.8x + 6y = 10 and 6x + 8y = −24 →
  25. 25.4x − y = 27 and x + 4y = 11 →
  26. 26.2x + 6y = 20 and 4x + y = 29 →
  27. 27.4x + 5y = −16 and x − 5y = 46 →
  28. 28.5x + y = 40 and 4x − 2y = 46 →
  29. 29.8x + 9y = 7 and 9x + 8y = 10 →
  30. 30.x − 5y = −10 and 3x + 4y = 27 →
  31. 31.5x + y = 36 and 4x − y = 27 →
  32. 32.4x + 7y = 71 and 7x + 4y = 50 →
  33. 33.2x + 6y = 62 and 6x + 2y = 58 →
  34. 34.5x + 8y = 92 and 8x + 5y = 77 →
  35. 35.4x + 2y = 10 and 6x − y = 43 →
  36. 36.8x + 3y = −9 and 3x + 8y = 31 →
  37. 37.4x + 3y = 21 and 5x + y = 18 →
  38. 38.6x + 6y = 54 and 5x + 4y = 44 →
  39. 39.x − y = −1 and 3x + 3y = −21 →
  40. 40.5x − 4y = 26 and 4x + 3y = 27 →

Answer key

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

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