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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 66 · 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 = 11 and 5x + 6y = −17 →
  2. 2.6x + y = 26 and 2x + 2y = 12 →
  3. 3.x + 6y = 51 and 6x + y = −9 →
  4. 4.x + 2y = −10 and 3x + 3y = −3 →
  5. 5.x + 5y = 16 and 3x − y = −16 →
  6. 6.4x − 4y = 32 and 4x + y = 37 →
  7. 7.x + y = 11 and x + 4y = 32 →
  8. 8.6x − 5y = 9 and 2x − 3y = −1 →
  9. 9.x + 3y = 3 and 3x + 5y = 13 →
  10. 10.3x + 5y = −7 and 5x + 3y = −1 →
  11. 11.3x + 4y = −7 and 2x + 2y = −6 →
  12. 12.x + 4y = 40 and 4x + 5y = 72 →
  13. 13.7x + 2y = −31 and 2x + 7y = 4 →
  14. 14.5x + 3y = 7 and x + 6y = −4 →
  15. 15.x + 2y = 12 and 2x + y = 18 →
  16. 16.2x − 5y = −18 and 6x + 4y = −16 →
  17. 17.2x + 3y = 11 and 3x + 2y = 9 →
  18. 18.6x + 8y = −56 and 8x + 6y = −70 →
  19. 19.3x − 4y = 59 and 6x + 5y = 14 →
  20. 20.x − 4y = −1 and 3x + 4y = 13 →
  21. 21.4x + 5y = 23 and 2x + 5y = 29 →
  22. 22.4x + 3y = 40 and 6x − 3y = 0 →
  23. 23.2x − 3y = −4 and 5x + 2y = 28 →
  24. 24.4x − y = 36 and x − 5y = 28 →
  25. 25.8x + y = 68 and x + 8y = −23 →
  26. 26.6x + 3y = 15 and 5x + 4y = 26 →
  27. 27.8x + 6y = 22 and 6x + 8y = 34 →
  28. 28.x + y = 11 and 4x + 2y = 26 →
  29. 29.6x − 3y = −27 and 4x + 4y = 12 →
  30. 30.2x − 6y = −34 and 4x + 5y = 34 →
  31. 31.4x + 9y = 13 and 9x + 4y = 13 →
  32. 32.5x + 7y = 27 and 7x + 5y = 33 →
  33. 33.4x + y = 20 and x + 4y = 35 →
  34. 34.3x − 2y = −5 and 6x − 3y = −3 →
  35. 35.2x + 2y = −2 and 6x + 3y = −9 →
  36. 36.x − 5y = −39 and 6x − y = −31 →
  37. 37.5x + 6y = −23 and 2x − 6y = −26 →
  38. 38.8x + 3y = 69 and 3x + 8y = 74 →
  39. 39.3x + 2y = −15 and 2x + 3y = −20 →
  40. 40.4x + 4y = −28 and x + 2y = −15 →

Answer key

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

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