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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 11 · 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 + 4y = 37 and 6x + y = 15 →
  2. 2.6x + 4y = 50 and 4x + 6y = 50 →
  3. 3.2x + 3y = −1 and 3x + 2y = 11 →
  4. 4.6x + 6y = −30 and 6x + 4y = −26 →
  5. 5.2x + y = 8 and x + 2y = −2 →
  6. 6.4x + y = 13 and 2x − 5y = 45 →
  7. 7.6x + 6y = −30 and 5x + y = −17 →
  8. 8.6x + 4y = 54 and 4x + 6y = 56 →
  9. 9.5x − 3y = 42 and 3x + 6y = 33 →
  10. 10.x + 3y = 15 and 3x + y = 29 →
  11. 11.x + 6y = −10 and 6x − 6y = −18 →
  12. 12.2x + 6y = 18 and 3x + 3y = 15 →
  13. 13.2x + 2y = 0 and 3x + 2y = −1 →
  14. 14.3x + 8y = −71 and 8x + 3y = −61 →
  15. 15.6x + 6y = 0 and 3x + 6y = 15 →
  16. 16.x − y = 4 and 6x + y = −25 →
  17. 17.4x + 8y = 64 and 8x + 4y = 44 →
  18. 18.3x + 4y = 22 and 4x + 3y = 20 →
  19. 19.6x + 2y = −6 and x + 2y = 9 →
  20. 20.7x + 6y = 78 and 6x + 7y = 78 →
  21. 21.4x + 5y = 37 and x + 3y = 11 →
  22. 22.x + 3y = 21 and 6x + 4y = 42 →
  23. 23.8x + 9y = 57 and 9x + 8y = 62 →
  24. 24.8x + 9y = −19 and 9x + 8y = −15 →
  25. 25.7x + 2y = 67 and 2x + 7y = 32 →
  26. 26.3x + 9y = 6 and 9x + 3y = −30 →
  27. 27.5x + 4y = 34 and 4x + 5y = 38 →
  28. 28.6x + 4y = 26 and 4x + 6y = 44 →
  29. 29.5x − 2y = 1 and 2x − y = −1 →
  30. 30.5x + y = −4 and 4x − y = −5 →
  31. 31.2x + 3y = −28 and 2x + 6y = −52 →
  32. 32.4x − 6y = 24 and 2x + 6y = 30 →
  33. 33.6x + 2y = −30 and x + 2y = 10 →
  34. 34.x + 4y = −32 and 3x − 4y = 16 →
  35. 35.3x − y = 11 and 3x + 5y = 53 →
  36. 36.6x + 4y = 12 and 4x + 6y = 38 →
  37. 37.x + 5y = 29 and 5x + y = 1 →
  38. 38.2x + y = −5 and x + 2y = 11 →
  39. 39.5x + 7y = 39 and 7x + 5y = 45 →
  40. 40.5x + y = 8 and 3x + 5y = −4 →

Answer key

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

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