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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 57 · 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 = 32 and 4x + 4y = −40 →
  2. 2.2x + y = 7 and x + 2y = 8 →
  3. 3.6x + 4y = −68 and 4x + 5y = −57 →
  4. 4.5x + 2y = −39 and 2x + 5y = −3 →
  5. 5.x + 3y = 31 and 2x + y = 17 →
  6. 6.6x + y = −18 and x + 6y = 32 →
  7. 7.6x + y = 2 and 6x + 2y = −2 →
  8. 8.8x + 4y = 0 and 4x + 8y = 36 →
  9. 9.x − 3y = −17 and 4x + 4y = 12 →
  10. 10.5x + 4y = 1 and 4x + 5y = −10 →
  11. 11.3x + 6y = 45 and 6x + 3y = 63 →
  12. 12.x + 4y = 18 and 4x + y = 12 →
  13. 13.4x + 5y = 47 and 6x + 3y = 39 →
  14. 14.4x + 6y = −16 and 2x + 4y = −6 →
  15. 15.6x − 5y = −12 and 3x − y = 3 →
  16. 16.4x + 3y = −1 and 3x + 4y = 1 →
  17. 17.3x + y = 29 and 3x + 4y = 44 →
  18. 18.4x + 8y = 64 and 8x + 4y = 80 →
  19. 19.2x − y = 19 and 5x − y = 37 →
  20. 20.6x − 4y = −30 and 4x + 4y = 20 →
  21. 21.4x + 6y = −26 and 6x − 5y = −53 →
  22. 22.4x + 4y = 36 and 3x − y = −5 →
  23. 23.6x + 2y = 36 and 2x + 6y = 60 →
  24. 24.x + 4y = 36 and 2x − 6y = −26 →
  25. 25.2x + 5y = −13 and 2x − 2y = 8 →
  26. 26.4x + 6y = 32 and x − 4y = −25 →
  27. 27.2x + y = 5 and 2x + 4y = 14 →
  28. 28.3x + y = 1 and 3x + 2y = −1 →
  29. 29.5x + 2y = 43 and 6x − y = 55 →
  30. 30.3x + 4y = 10 and 4x − y = 7 →
  31. 31.9x + 7y = −35 and 7x + 9y = −13 →
  32. 32.9x + 4y = 108 and 4x + 9y = 113 →
  33. 33.2x + 3y = 25 and 3x + 2y = 20 →
  34. 34.x + 6y = 59 and 3x + 5y = 60 →
  35. 35.9x + 5y = 43 and 5x + 9y = 55 →
  36. 36.3x + y = 17 and x + 3y = 3 →
  37. 37.x − y = 12 and 3x + 6y = −9 →
  38. 38.6x + y = 11 and x + 6y = −4 →
  39. 39.7x + 6y = 43 and 6x + 7y = 35 →
  40. 40.9x + y = 31 and x + 9y = 39 →

Answer key

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

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