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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 652 · 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 + 5y = 37 and 2x + 2y = 18 →
  2. 2.5x + y = 21 and 5x + 5y = 25 →
  3. 3.4x + y = 1 and x + 4y = −11 →
  4. 4.3x − 4y = −30 and 5x − 6y = −48 →
  5. 5.2x + 9y = 66 and 9x + 2y = 66 →
  6. 6.2x + 4y = −10 and 4x + 6y = −22 →
  7. 7.6x + 7y = 41 and 7x + 6y = 50 →
  8. 8.3x + 7y = 78 and 7x + 3y = 62 →
  9. 9.5x − y = 33 and 2x + 3y = 20 →
  10. 10.x + 4y = 3 and 2x + 6y = 0 →
  11. 11.4x − 6y = −26 and 5x + 3y = −1 →
  12. 12.x + 3y = 16 and 3x + y = 24 →
  13. 13.5x + 6y = 13 and 2x + y = 8 →
  14. 14.x + y = 17 and x − 5y = −31 →
  15. 15.2x + 2y = 36 and 2x − 5y = −27 →
  16. 16.6x + 2y = −28 and 2x + 6y = 28 →
  17. 17.6x + 7y = 43 and 7x + 6y = 48 →
  18. 18.2x + 5y = 24 and x − 3y = 1 →
  19. 19.4x + 2y = −42 and 2x + 3y = −31 →
  20. 20.7x + 8y = −9 and 8x + 7y = −6 →
  21. 21.4x + 5y = −19 and 5x + 4y = −26 →
  22. 22.2x + y = 12 and x + 2y = 18 →
  23. 23.5x + 9y = −23 and 9x + 5y = 37 →
  24. 24.5x − y = −27 and 6x + y = −28 →
  25. 25.5x + y = 8 and 3x + 4y = 15 →
  26. 26.6x + 6y = −42 and 4x − 4y = 36 →
  27. 27.2x + 6y = 48 and 4x + 5y = 47 →
  28. 28.4x + 9y = −5 and 9x + 4y = −60 →
  29. 29.x + 6y = −3 and 6x + 4y = 14 →
  30. 30.4x + 5y = −67 and x − 4y = 20 →
  31. 31.5x + 2y = 36 and 5x − 3y = 21 →
  32. 32.7x + 6y = 49 and 6x + 7y = 55 →
  33. 33.5x + 6y = −22 and 2x + 5y = −27 →
  34. 34.3x + 6y = 18 and 2x + 2y = 8 →
  35. 35.2x − y = 7 and 5x + y = 7 →
  36. 36.7x + 2y = 49 and 2x + 7y = 59 →
  37. 37.6x + 4y = −62 and 3x − 4y = 17 →
  38. 38.2x + 6y = 60 and x + y = 14 →
  39. 39.2x + 3y = 4 and 3x + 2y = −4 →
  40. 40.6x + y = 49 and x + 2y = 21 →

Answer key

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

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