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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 602 · 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. 1.5x + 2y = 50 and 3x + 4y = 44 →
  2. 2.6x − 3y = 57 and 6x + y = 21 →
  3. 3.2x + y = 11 and 6x − 5y = −23 →
  4. 4.3x + 3y = 51 and 3x + 4y = 59 →
  5. 5.4x − 2y = 26 and 5x + 3y = 16 →
  6. 6.2x + 3y = −24 and 2x − 6y = 30 →
  7. 7.6x + 5y = 46 and 6x − 4y = −26 →
  8. 8.4x − 5y = 31 and 4x + y = 13 →
  9. 9.5x + 7y = 34 and 7x + 5y = 38 →
  10. 10.2x − 2y = −8 and 2x − 4y = −24 →
  11. 11.3x + 3y = −33 and 3x − y = −25 →
  12. 12.3x + 2y = 1 and 6x + 2y = −2 →
  13. 13.8x + 6y = −34 and 6x + 8y = −36 →
  14. 14.x + 3y = 19 and x + y = 9 →
  15. 15.6x + 2y = −34 and 2x + 6y = 26 →
  16. 16.2x − y = 0 and 6x − 5y = −8 →
  17. 17.x + 3y = −16 and 3x + y = −8 →
  18. 18.4x + 2y = −12 and 2x + 4y = −18 →
  19. 19.x + 4y = 21 and 6x − 3y = 18 →
  20. 20.6x + 4y = 66 and x + 5y = 50 →
  21. 21.5x + 3y = 34 and 3x + 2y = 22 →
  22. 22.x + y = 12 and 3x + 2y = 28 →
  23. 23.2x + 2y = 0 and 2x + 5y = −3 →
  24. 24.5x + 6y = 67 and 5x + 2y = 39 →
  25. 25.4x + 3y = −15 and x + 4y = 19 →
  26. 26.4x − y = −9 and 4x + 5y = 21 →
  27. 27.2x − 2y = −8 and x + 3y = 24 →
  28. 28.2x + 6y = 48 and 6x + 2y = 64 →
  29. 29.9x + 7y = 79 and 7x + 9y = 65 →
  30. 30.3x + y = 11 and 4x + 4y = 28 →
  31. 31.x + 9y = 70 and 9x + y = 70 →
  32. 32.5x + y = 28 and x + 5y = 44 →
  33. 33.9x + y = −21 and x + 9y = 51 →
  34. 34.2x − 3y = 33 and 4x − 4y = 48 →
  35. 35.8x + 5y = 60 and 5x + 8y = 57 →
  36. 36.3x + y = 10 and x + 3y = 22 →
  37. 37.7x + 3y = 69 and 3x + 7y = 81 →
  38. 38.2x − 6y = 22 and 6x + 6y = 42 →
  39. 39.x + y = −12 and 6x + 2y = −36 →
  40. 40.x + 5y = 26 and 5x + y = −38 →

Answer key

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

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