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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 95 · 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. 1.4x + y = 14 and 6x + 2y = 24 →
  2. 2.2x + 8y = 80 and 8x + 2y = 80 →
  3. 3.2x − 2y = 26 and 5x + y = 41 →
  4. 4.2x + y = 2 and x + 2y = 10 →
  5. 5.x + y = 6 and 6x − 2y = 44 →
  6. 6.6x − 4y = −22 and 6x − 2y = −8 →
  7. 7.4x + 2y = 28 and 2x + 4y = 20 →
  8. 8.6x + 5y = −9 and 5x + 6y = 9 →
  9. 9.x + 5y = 41 and 5x + y = −11 →
  10. 10.3x + 6y = −45 and x − 6y = 49 →
  11. 11.6x + y = 5 and 2x + 5y = −31 →
  12. 12.5x − 3y = −67 and 2x + y = −7 →
  13. 13.x − 2y = −4 and 3x + 4y = 28 →
  14. 14.4x + 7y = −35 and 7x + 4y = 13 →
  15. 15.4x + 6y = 80 and 6x + 4y = 80 →
  16. 16.x + 8y = 15 and 8x + y = −69 →
  17. 17.5x + y = −22 and 2x + 5y = 5 →
  18. 18.5x − y = −31 and 6x − y = −36 →
  19. 19.2x + 6y = −48 and 6x + 6y = −72 →
  20. 20.3x − 6y = 27 and 6x + 4y = 6 →
  21. 21.7x + y = 47 and x + 7y = −7 →
  22. 22.6x + 9y = 48 and 9x + 6y = 57 →
  23. 23.6x − 5y = 10 and 4x − 5y = 0 →
  24. 24.2x + 2y = 2 and x + 6y = −14 →
  25. 25.x − 3y = 5 and x − y = 7 →
  26. 26.5x − 2y = 4 and 2x + y = 7 →
  27. 27.3x − 3y = 0 and 2x + 5y = −28 →
  28. 28.3x + 8y = 34 and 8x + 3y = −1 →
  29. 29.2x + 4y = 10 and 4x + 3y = 15 →
  30. 30.7x + 3y = −10 and 3x + 7y = −50 →
  31. 31.x + 6y = −57 and 4x + y = −21 →
  32. 32.5x − 3y = 27 and x + 2y = 21 →
  33. 33.6x + 7y = 41 and 7x + 6y = 37 →
  34. 34.3x − 6y = 45 and x − y = 11 →
  35. 35.4x − 2y = 28 and x + 2y = −13 →
  36. 36.x − 4y = −14 and 6x + 6y = 66 →
  37. 37.5x + 2y = 46 and x + y = 11 →
  38. 38.x + 3y = 11 and 3x + y = 17 →
  39. 39.2x + y = −11 and 5x + 3y = −32 →
  40. 40.2x + 3y = 25 and 2x + 2y = 18 →

Answer key

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

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