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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 713 · 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. 1.2x − 2y = −24 and 2x + 2y = −4 →
  2. 2.4x + 2y = −52 and 2x + 4y = −50 →
  3. 3.6x + 2y = 48 and 4x + 5y = 54 →
  4. 4.5x − 5y = −40 and 2x − 6y = −40 →
  5. 5.5x − y = 17 and 6x + y = 5 →
  6. 6.2x + 2y = −10 and 4x − y = 15 →
  7. 7.4x + 4y = 16 and 5x − 6y = −57 →
  8. 8.5x + 2y = 41 and 2x + 5y = 29 →
  9. 9.6x + y = −53 and 4x + 2y = −42 →
  10. 10.x + 3y = −13 and 5x − 6y = −23 →
  11. 11.3x − 3y = −12 and 4x − 3y = −11 →
  12. 12.x + y = 7 and 6x + 5y = 41 →
  13. 13.4x + 2y = 26 and 3x − 3y = 42 →
  14. 14.x + 6y = −50 and 4x + 5y = −48 →
  15. 15.2x + 9y = 11 and 9x + 2y = 11 →
  16. 16.x + 9y = 73 and 9x + y = 17 →
  17. 17.x + 8y = 65 and 8x + y = −47 →
  18. 18.x + 5y = −22 and 4x − y = 38 →
  19. 19.5x − 4y = −3 and 2x − y = 0 →
  20. 20.6x + 2y = 20 and 5x − 4y = 11 →
  21. 21.2x − 2y = −8 and 2x − 6y = −4 →
  22. 22.4x + 5y = −11 and 5x + 4y = −25 →
  23. 23.5x − 6y = −76 and 3x + 6y = 12 →
  24. 24.4x + y = −9 and 4x − y = −15 →
  25. 25.7x + 2y = −3 and 2x + 7y = 57 →
  26. 26.5x + 2y = 56 and 2x + 5y = 56 →
  27. 27.2x + 6y = 28 and 2x + 2y = 12 →
  28. 28.2x + 6y = 24 and x − y = 8 →
  29. 29.x + 7y = 56 and 7x + y = −40 →
  30. 30.2x + 6y = 20 and 6x + 6y = 24 →
  31. 31.5x + 5y = 65 and x + 6y = 38 →
  32. 32.3x + 6y = 15 and 6x + 3y = −33 →
  33. 33.x + 7y = 57 and 7x + y = −33 →
  34. 34.4x + 2y = 36 and 2x + 4y = 30 →
  35. 35.8x + 4y = 76 and 4x + 8y = 56 →
  36. 36.2x + 9y = −73 and 9x + 2y = 18 →
  37. 37.x − 6y = 19 and 5x − 3y = 41 →
  38. 38.x + 6y = −8 and 5x + 6y = 8 →
  39. 39.9x + 7y = 58 and 7x + 9y = 38 →
  40. 40.5x − 5y = −30 and 3x − 5y = −28 →

Answer key

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

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